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Henrtj W. Sage 




Cornell University Library 
UF520 .B89 

A text-book of ordnance and gunnei 


3 1924 030 759 645 

iery : 


The original of this book is in 
the Cornell University Library. 

There are no known copyright restrictions in 
the United States on the use of the text. 





Ordnance Department, U. S. Army, 
Instructor of Ordnance and Gunnery at the U t S. Military Academy', 





London i CHAPMAN & HALL, Limited. 


Copyright, 1896, 





The present text-book has been compiled with the object 
of presenting as clearly as possible the elementary principles 
of the course in Ordnance and Gunnery as taught at the 
Military Academy, and of so arranging it that it can be 
readily used for recitations in the section-room. For this 
purpose it has been divided into separate subjects, each as 
well defined as possible. In its preparation I have followed 
the lines laid down by my predecessor Capt. Henry Met- 
calfe, U. S. A., retired, from whose labors in the same field I 
have derived the greatest assistance. I am also under many 
obligations to those who have kindly criticised and cor- 
rected my work in many important particulars, and especi- 
ally to Colonel Buffington, Captains Smith, Blunt, Birnie, 
Mitcham and Crozier, Ordnance Department, and to Mr. 
W. R. Quinan of the California Powder Company. 

Lieut. Babbitt, Ordnance Department, my assistant at 
the Military Academy, has made many valuable criticisms 
and suggestions which have added greatly to the clearness 
of the work. 

West Point, March 10, 1896. 




Gunpowder and Interior Ballistics i 

High Explosives and Smokeless Powders 105 

Guns 136 

Projectiles and Armor 279 

Fuzes and Primers 328 

Exterior Ballistics 347 

Artillery Carriages ; Theory of Recoil 389 

Pointing ; Probability of Fire 466 

Portable Arms 528 

Machine and Rapid-fire Guns 589 

Index 639 





1. Composition — Manufacture. 

Composition. — Gunpowder is a mechanical mixture of 
nitre, charcoal, and sulphur, in the proportions of 75 parts 
nitre, 15 charcoal, and 10 sulphur. 

The nitre furnishes the oxygen to burn the charcoal and* 
sulphur. The charcoal is the principal combustible body,, 
and the suiphur gives density to the grain and lowers its 
point of ignition. 

The nitre is purified by solution in water and crystalliza- 
tion, the sulphur by distillation, and the charcoal is care- 
fully prepared to make it as uniform as possible. 

The distinguishing characteristic of charcoal is its color,, 
being brown when prepared at a temperature up to 280 
Cent., from this to 340° red, and beyond 340 black. 

Brown charcoal is now generally used for powder. 

Manufacture. — The operations are : 

1. Pulverizing, mixing, and incorporating the ingre- 

2. Compressing this mixture to give it a proper density. 

3. Dividing the dense mass into grains. 

4. Finishing the grains. 

Pulverizing and Mixing. — The nitre is in fine crystals 
when received ; the sulphur is rolled in an iron barrel with , 


rollers running in a 

Fig. i. 

iron balls ; and the charcoal also, or the latter may be 
ground in a mill. 

The ingredients are mixed by hand or by machine. 

Incorporating.— To make the mixture thorough, the above 

composition is moistened and incorporated in a wheel mill. 

This mill consists of a pair of heavy cast-iron cylindrical 

circular trough (Fig. i). By their 

action they grind the products 

together, and give a thorough 


This is the most important 
operation in the manufacture, 
and if not well done no subse- 
quent operation can remedy it. 

Pressing. — The mill-cake which 
comes from the " wheel mill " is 
broken up, moistened, and placed, 
in layers about 2 inches thick, 
under a hydraulic press. The 
layers are reduced to a thickness of about 1 inch and be- 
come very dense and hard, and this is called " press-cake." 

Graining. — In ordinary powders, the press-cake is broken 
up into grains of various sizes. The object of this is to 
increase the surface of combustion, and to regulate it 
according to the gun in which it is to be used. The grain- 
ing is done by rollers acting on the press-cake, and the 
grains are afterwards assorted with sieves. 

Glazing. — To remove the sharp angles, and give uniform 
density to the surface, the grains are placed in a wooden 
barrel revolving on its axis. They are thus made to rub 
against each other, and accomplish, by their mutual attrition, 
the objects mentioned. 

Drying and Dusting.— The excess of moisture in the 
powder is now removed by a current of warm, dry air, and 
the dust which has been formed on the grains is removed 
by passing them through a revolving sieve. 

Blending and Marking.— different lots of the same kind 
of powder are mixed, to overcome, as much as possible, 
irregularities of manufacture. In our service the powder 


is packed in ioo-lb. barrels and marked with certain letters, 
as I. K. B., E. V. X., etc., the first two letters denoting the 
kind of powder, or its use, and the third letter the lot. 

In foreign services the letters indicate the use directly: 
as, R. F. G., rifle fine grain ; P., pebble ; etc. 

Government powder is purchased by contract. 

2. Specific Gravity and Gravimetric Density. 

The Specific Gravity, or actual density, of gunpowder, 
like that of any solid body, is the weight of a given volume 
referred to that of an equal volume of water as unity. 
Since water dissolves the nitre, mercury is used instead. 
The instrument employed is called a mercury densimeter, 
and consists of a glass globe a, Fig. 
2, connected with an air-pump by 
a rubber tube c. 

The globe is exhausted of air 
and its lower end immersed in 
mercury in the dish d. 

The mercury is allowed to rise 
till it fills the globe and stands at 
a certain height in the glass tube 
e. The globe is then detached 
full of mercury and weighed. It 
is then emptied, and a given 
weight of powder placed in it, re- 
turned to its original position, the 
air again exhausted, and mercury 
allowed to enter till it stands at 
the same height as before; the 
globe with its mercury and pow- 
der again detached and weighed. 
The difference of the two weights 
of mercury gives the weight of the mercury whose volume 
is equal to that of the powder. 

Let a = the weight of the powder; 

P = the weight of the vessel and mercury; 

P = the weight of the vessel, mercury, and powder ; 

Fig. 2. 


S = the specific gravity of the mercury ; 
8 = the specific gravity of the powder. 

Then P - a — the weight of the mercury and vessel 
when the latter is partially filled with 
powder ; 
p — p' _|_ a = the weight of the volume of mercury 
displaced by the powder. 

Since the weights of equal volumes are proportional to 
the densities, we have 

a : P - P' + a : : 8 : S, 


S =P^h-a 0) 

The density varies between 1.68 and 1.85. 

Gravimetric Density is the name given to the density of 
powder when the spaces between the grains are considered. 
That is, it is the specific gravity of the powder in its natural 
form. Suppose we have a solid piece of powder weighing 
1 lb. If we determine its specific gravity, we will obtain a 
value 8 given by formula (1). Suppose the same powder 
broken up into grains. Its weight will not change, but its 
volume will be greater than before. If we determine its 
specific gravity under these circumstances, by comparing its 
weight with the weight of an equal volume of water, we have 
a particular value, called the " gravimetric density." 

It is evident that the same powder will have only one 
value for 8, but may have many values for gravimetric den- 
sity according to its granulation. If the shape of the grain 
is changed, the same weight of powder will occupy a greater 
or less space according as the spaces between the grains are 
greater or less. 

Hence we say that gravimetric density measures the ca- 
pacity of powder to pack, or measures the spaces between 
the grains. 

A cubic foot, of powder is usually taken in determining 


gravimetric density. A cubic foot of water weighs 62.425 
lbs. Hence we have 


'=5^S\ (2) 

y denoting the gravimetric density, and w the weight of a 
cubic foot of powder, y varies between 0.875 an d 1.00. 

The space actually occupied by the solid powder in a 
given volume is determined as follows: 

Let V= the total volume occupied by the powder; 
v = the volume of the solid powder. 

Since volumes are inversely as densities, we have 

V:v::S :y; 

*=V Y S (3) 

If y = 1.00 and S = 1.8 (the ordinary values), we have 

v = .&V. (4) 

That is, the volume occupied by the solid powder in a 
charge is about .56 of the total volume of the charge. 

3. Form of Grain. 

Irregular Granulation. — The processes of manufacture 
are the same for all powders up to and including incorpo- 

If the mill-cake be pressed into slabs, and these slabs 
broken up into irregular grains by rollers, we have powders 
of " irregular granulation." In our service the powders of 
irregular granulation are : 

(a) Small-arms pozvder, used in the Springfield rifle and 
carbine, and in small arms generally, and also as a bursting- 
charge in field-shells. 

(b) Mortar-powder, used in the 3.00-inch wrought-iron rifle, 
in the siege and sea-coast smooth-bore mortars, and in their 

(c) Cannon-powder, used in the old 8- and 10-inch smooth- 
bore guns. 


(d) Mammoth Powder, used in the 15-inch Rodman guns. 

(e) I. K. Powder, used in the 3.20-inch steel B. L. rifle,. 
model of 1885, charge (3.50) lbs. 

All these powders may be regarded as having grains, 
which approach a sphere in shape, and whose mean radius 
is determined as follows : 

Let N = the number of grains in one pound of powder ; 
r — the mean radius of the grain in inches ; 
8 = the specific gravity of the powder. 
The volume of one grain is 

V=i*r°- ( S> 

Its weight is (Michie, eq. 1) 

W=V8g>, (6) , 

g' being the weight of one cubic inch of water, or 

, _ 62.425 


ff /_ ***** X 62.425 

1728 y7> 

and the weight of N grains is 

]\t W - §nr*8 x 62.425 X N 

1728 .... 

ButiVrj^=i. Hence 

, _ j*r'3 x 62425 X N 


{SN)i (9> 


Using this method, we find 

2r = 0.04 small-arms powder ; 
2r ~ 0.08 mortar powder ; 
2r = 0.30 cannon powder; 
2r = 0.75 mammoth powder ; 
2r = 0.24 I. K. powder. 



Regular Granulation. — Powders of regular granulation are 
obtained by breaking up the mill-cake and pressing it be- 
tween plates having depressions in them of regular shape, 
such as a sphere or a pyramid. 

Under this head we have the Dupont powders, viz.; 

(a) The Hexagonal. — The shape of the grains is that of 
two hexagonal pyramids joined base to 
base. The grains are connected by a thin 
cake, which is broken off, and leaves a 
rough surface at a, which facilitates ig- 
nition. Used in the 8-inch converted rifle, 
charge 35 lbs. Fig. 3.— Hexagonal. 

(b) The Sphero-hexagonal, Fig. 4, which is the same as 
the above, except that spheres are substi- 
tuted for hexagonal pyramids. 

This powder is now used for all the field 
and siege guns and mortars. In the field 
service it has replaced the I. K. powder used 
with the earlier model guns. 
Molded Pozvder. — This is made by reducing the mill-cake 
to powder and pressing it into any required form, each grain 
being made separately ; or a number of grains of powder of 
irregular granulation may be compressed into a single large 
grain ; the latter is also called concrete powder. Under 
this head we have prismatic or brown powder, which is a 
molded concrete powder made as above described. It is 
called brown or cocoa powder from its color, which is due 
to brown charcoal. 

It is made in hexagonal prisms, Fig. 5, about 1 inch high 
and 1.375 inches between opposite 
faces. Each prism is pierced by a 
central hole parallel to the axis, and 
about 0.40 inch in diameter. The 
composition is generally given as 

Nitre 81.5 per cent 

Charcoal 15.5 per cent 

Sulphur 3.0 per cent 

Fig. 4. — Sphero 



Fig. 5. — Cocoa. 



It is a slow-burning powder, and is used in modern high- 
power guns of large calibre. 

4. Inspection and Proof of Powder— History. 

Inspection.— The object is to see that the powder is 
properly manufactured, and that it has certain required 


For small-arms powder ioo barrels are considered a lot, 
and from them five barrels are taken, one pound of powder 
from each barrel being selected for test. If the test is suc- 
cessful, the lot is accepted. 

For Granulation. — All grains must pass through a sieve 
with a mesh of 0.06 inch and none through a mesh of 0.03 

Specific Gravity between 1.75 and 1.80 and gravimetric 
density between 0.96 and 1.00. 

Dust is detected by allowing a stream of powder to fall 
rapidly two or three feet in a strong light. There must be 
no dust. 

Incorporation is tested by flashing 20 grains of powder on 
a copper plate. There should be little residue, and no 
globules of fuzed nitre on the plate. 

Moisture is determined by exposing 1000 grains to a tem- 
perature of ioo° F. for 24 hours. The loss in weight should 
be about 7 grains. 

Capacity for absorbing moisture is tested by exposing 
1000 grains to the vapor of water for 24 hours. The gain in 
weight should be about 6 grains. 

Fouling is tested by firing rapidly 100 rounds of rifle-ball 
cartridges in series of 25 rounds each and weighing the rifle 
after each series. In a moderately dry atmosphere the weight 
of fouling from the 100 rounds should not exceed 15 grains. 

For other powders the inspection will vary according to 
the terms of the contract. 

Proof. — The object of proving powder is to ascertain the 
initial velocity it will impart to the projectile, the corre- 
sponding pressure on the bore, and, for small arms, the 
accuracy of the projectile. 

The powder is always proved in the gun in which it is 


to be used, and with service charges. The velocities and 
pressures are measured with instruments to be described. 

HISTORY. — Gunpowder was first used in Europe early in 
the fourteenth century, and in the form of powder or dust, 
whence the name. The guns in which it was used were 
weak, and the powder was suited to them, because it burned 
slowly and gave low pressures. In the form of dust, how- 
ever, it was difficult to load at the muzzle, as cartridges were 
not used, and hence loading at the breech was introduced. 
This failed because no gas-check could be devised that 
wOuld completely close the breech. As guns improved in 
strength, better results were obtained by graining the pow- 
der, but the grained powder became too strong for the guns, 
and large guns were not made. No marked change in pow- 
der was made until about i860. 

General Rodman, of the Ordnance Department, then 
. proposed to vary the size of the grain with the calibre, using 
large-grained powder for large guns. He also advocated a 
perforated powder, which was not used. His mammoth 
powder, however, was adopted, and by an improvement in 
the process of gun-construction, together with that of the 
powder, he built smooth-bore guns up to 20 inches in calibre. 

Following Rodman's plan, various forms of powder have 
been adopted by other nations, the general idea being to so 
modify the action that the gun will be strained less at the 
beginning of the motion of the projectile, and more uni- 
formly throughout the bore, than with the old powders. 
The brown powder is the latest development of the old 
nitrate powders. It has, however, many objections, and at 
present smokeless powders are being developed, with the 
prospect that they will supersede the others. 

5. Combustion in Air — Laws. 

Explosion is the rapid conversion of gunpowder into 
gases and solids with evolution of heat. It may be divided 
into three parts, Ignition, Inflammation, and Combustion. 

Ignition is the setting on fire of a part of the grain or 
charge, and for this purpose a temperature of 300 C. is 


Gunpowder may be ignited by electricity, by contact 
with an ignited body, by friction, shock, or by chemical 

A gradual heat will decompose the powder by subliming 
the sulphur, and the temperature of ignition will be raised 

Flame, owing to its slight density, will not ignite powder 
readily. The time necessary for ignition will vary with 
the condition of the powder. Thus damp powder ignites 
less easily than dry ; a smooth grain less easily than a rough 
one ; a dense grain less easily than a' light one ; etc. 

Powder is ordinarily ignited by a primer, by electricity,, 
or by contact with an ignited body. 

Inflammation is the spread of the ignition from point to 
point of the grain, or from grain to grain of the charge. 

With small-grain powders, where the spaces between 
grains are small, the time of inflammation is large as com- 
pared with the time of combustion of a grain, but with 
modern large-grain powders, the facilities for the spread of 
ignition and the time of burning of the grain are so great, 
that' the whole charge is supposed to be inflamed at the 
same instant, and the time of inflammation is not considered. 

Combustion is the burning of the inflamed grain from the 
surface of ignition inward or outward or both, as the case 
may be. 

Laws. — Experiment shows that powder burns in the air 
according to the following laws : 

i. In parallel layers, with uniform velocity, and the 
velocity is independent of the cross-section burning. 

2. The velocity of combustion varies inversely with the 
density of the powder. 

Hence if v denote the velocity of combustion, and 8 the 
density of the powder, we have 

vS = c, (10) 

the constant c depending on the nature of the powder. 

3. The velocity decreases rapidly as the degree of moist- 
ure in the powder increases. 


4. It increases with the amount of trituration of the in- 
gredients, up to a certain limit. 

5. For the same density, trituration, and moisture, the 
greatest velocity of combustion is obtained with a powder 
whose composition is 75 nitre, 15 charcoal, and 10 sulphur. 

6. In air the actual velocity of combustion is from 0.4 to 
0.6 inch per second. 

7. The velocity varies with the pressure according to a 
law which is expressed by the following formula of Sar- 


in which v is the velocity of combustion for the pressure 
p, and v Q the velocity in open air corresponding to the at- 
mospheric pressure /v 

According to this formula, a powder which burns 0.6 
inch per second in air would burn about 29 inches per 
second in a gun under a pressure of 35,000 lbs. per square, 

6. Formula for Burning in Air of Grains of Different Shapes. 

To deduce a formula for the amount of powder burned 
at the time t, we proceed as follows : 

The amount burned per unit weight or per unit volume 
at any time t will evidently be a function of /, and may be 
represented by </>(t). Suppose <p(t) to be developed accord- 
ing to the ascending powers of t, with constant coefficients, 
which are to be determined. We may then write 

^W = ~( I - A 7 + A 4 7+ etc -)> • • • • ( I2 ) 

in which a, \, and M are constants depending on the form of 
the grain, and r is the total time of combustion of the grain, 
and hence depends on its size. The negative sign is used be- 
fore X because the sign of this term is found to be negative 
for all forms of grain in use. It is required to find values 
for a, \, and fi for all service grains. 


Spherical Grain.— Let r be the radius of the grain ; 
v the velocity of combustion ; 
r the total time of combustion. 
The original volume of the grain is f tzt'. At the end 
of the time t the radial distance burned over is vt, and the 
radius remaining unburned is r — vt. Hence the volume 
unburned at the end of / is ^n(r — vt)*. 
The volume burned is then 


f 7tr 3 - i n{r - vt)', (13) 

[i-f 1 -^)] 04) 


* = £ (lS > 

and substituting for - in (14) its value from (15), we have 



[--(■-!)•] ™ 

The expression (16) is the actual volume burned at the 
end of the time t. It is composed of two factors, the first 
being the original volume of the grain, £ nr*, and hence the 
second factor must be the proportional part burned ; that is, 
the amount burned per unit of volume, or per unit of weight, 
in the time t, according as we consider volumes or weights, 
and is denoted by 0(/). Hence for this particular form of 
grain we have 




«<>=?(■ -;+;-?) W> 

Comparing this with the general development in equation 
(12), we see that 

a =3, \=i, /i = f 



Since all powders of irregular granulation may be con- 
sidered as spheres whose mean radii can be calculated by 
equation (9), and since the hexagonal and sphero-hexagonal 
may also be so considered, these values of a, A, and /* apply 
to all such powders. 

Values of a, K, and fx for Other Forms of Grain. — By a 
similar process we can find the values of a, A, and jx for all 
service grains. These values are collected in the following 

Form of Grain. 




Spherical "1 
Cubical I 


* + *+y 

I + 2X 






x+y + xy 

1 + x +y 

2X + X* 


Irregular t 
granulation J 



i +x+y 

X 1 

Flat, x — v — i. 

I -)- 2X 



I + 2X 

Pierced cylinder ) 

Cocoa ) 
Pierced cylinder; } 

I + .* 


half of height ) ' 


In this table x = 75, y — -, in which for the parallelopi- 
P y 

pedon a, /3, and y are the lengths of the edges of the grain, 
a being the least dimension ; also, for the pierced cylinder, 

r — r' 
x = ■ , in which r is the exterior and r' the interior 

radius of the cylinder, and h its height. 

By substituting for a, X, and fx in the general formula (12), 
the values given in the above table, the amount of powder 
burned, per unit weight, or per unit volume, for any of the 
above-shaped grains, can be determined ; and this atnount, 
multiplied by the total weight or volume, will give the total 
amount burned at any time t. 


7. Velocity of Emission — Spherical Grain. 

This is the rate of evolution of the gas of gunpowder ; 
that is, the ratio of the part of the unit of weight of powder 
burned in a small interval of time to that time. 
Considering unit weight, let 

v denote the velocity of combustion ; 
5 the total surface burning at any time t ; 
S the density of the powder. 
Then vdt is the space passed over by the burning surface 
in the time dt, Svdt the volume burned, and SvSdt the 
weight, the value of g' being unity for French measures. Then, 
from the definition, we have for the velocity of emission 

V = -^- = SvS (19) 

This equation shows that the velocity of emission de- 
pends upon — 

1. The total burning surface .S; 

2. The velocity of combustion v ; 

3. The density of the powder S. 

But it has been found by experiment that in air 

vS = c, (see equation (10).) 

The velocity of emission in air depends, therefore, upon 
the surface burning, and this surface depends on the form 
and size of the grain. . 

We may obtain another expression for the velocity of 
emission which is more convenient for discussion, as fol- 
lows : 

The proportional part of powder burned per unit weight 
at any time t is, as we have seen, a function of t, and has 
been expressed by tj>{t). 

The proportional part burned in the time dt is d[tp(t)], 
and by definition we have 

;_ dt (20) 

The value of <p{t) lor different forms of grain can be de- 
termined just as for the spherical grain, and knowing these, 

>f-^= -^1 -2^- + 3^— J. . . (20«) 


we can determine the values of the velocity of emission for 
different forms of grain. It is evident that the form of 
grain whose velocity of emission is least at first will be 
most advantageous, since, the rate of emission being small, 
the gas will be given off gradually at first, and the press- 
ure in the gun will increase slowly, and give time for the 
projectile to move before the gun is overstrained. 

We can therefore determine what form of grain is best 
calculated to give the lowest pressure. 

For Spherical Grain. — Differentiating equation (12) 
with respect to t, we have 


Substituting for a, \, and jjl their values for the spherical 
grain, viz., a = 3, A = i,;u = £, we have 

d[<p(t)] _ 3 /_ t y 

' dt r\ rT 

At the beginning of combustion, when t = o, we have 

and at the end, when t = r, 

T} = o. 

8. Velocity of Emission for Parallelopipedon and for Pierced Cyl- 

For Parallelopipedon. — Substituting the values of a, 
X, and a* for the parallelopipedon in (20a), we have 

_ d[_<j>{t)-\ _ l + x+ yf _ 2{x+y+ xy) t_ , yey f_\ 
V ~~d7 ~ r \ i+x+y r'T i + x+yr'l- 

When t = o, we have 

1 -\-x-\-y 
V= r —' 

and when t = t, 


For the flat grain whose thickness is one half its other 
dimensions, x = y = £. Hence for this grain we have at 
the beginning of combustion 


V = -. 

and at the end 


or the velocity of emission is less at the beginning and 
greater at the end for a flat grain than for a spherical one. 

For Pierced Cylinder— Cocoa Powder. — Substitut- 
ing the values of a, A, and fi for the pierced cylinder in (200), 
we have 

= rf[0(/)] = L±f d _ 2X *\ 

' dt T V I -f- X T ) 

When / = o, we have 

and when t = r, 


V = 4( J - *)• 

For this grain x = — y — . If x = J, as in the case of the 

flat grain, the thickness of the walls is one half the height* 
and we have, for the velocity of emission at the origin, 

and at the end, 

3 i-5 
V = — =— ; 
2T r 


Comparing this with the spherical and flat grains, we see 
that the velocity of emission for the pierced cylinder is less 
at the beginning and greater at the end than for any other 
form of grain. Hence, so far as velocity of emission is con- 
cerned, this is the best form of grain, and is the one now 
used in large guns. 


The results are shown in the following table : 


Form of Grain. 

Velocity of Emission 

at Beginning. 

Velocity of Emission 
at End. 

Spherical ) 
Irregular grain \ ' ' 


Pierced cylinder . . 








9. Size of Grain — Density — Progressive Powders. 

Size. — The velocity of emission depends on the surface in 
combustion, and this, as has been shown, depends on the form 
and size of grain. The effect of form has been discussed. 
To show the effect of size, suppose we have two charges of 
the same weight, composed of cubical grains. 

Let a represent the edge of the grains in the first 
charge ; 
2a the edge of the grains in the second charge ; 
N the number of grains in the first charge. 
The surface of each grain in the first charge will be 

and the total surface in the first charge 

S = Nx6a\ 

Since the weights are proportional to the cubes of the 

edges of the grains, each grain in the second charge will 


W _ o 
' a' 

times as much as those of the first charge, and hence there 

will be only — grains in the second charge. 


The surface of each grain in the second charge will be 
(2a)' X 6, 


and the total surface in the second charge 

y = fx6xw = ^ = f; 

or the total surface in the second charge will be only one 
half that in the first; and since the velocity of emission 
depends on the surface, it will be in the beginning one half 
that of the first charge. 

Influence of Density. — Considering a single grain, if 
we increase its density, the volume remaining constant, we 
decrease the velocity of combustion according to the formula 

vS = c, 

and hence do not change its velocity of emission, since 
r) = SvS. But considering a given weight of power, if we 
increase the density of the grains without changing their 
•volume, we increase the weight of each grain, and hence de- 
crease the number of grains contained in this weight. This 
decreases the initial surface of combustion in the given 
weight, and hence decreases the velocity of emission. 

Ordinarily, for slow emission we increase at the same 
time both the size and the density of the grain. The limit 
of increase in size and density is reached when the grains 
cannot be consumed in the gun before the projectile leaves 
the bore. 

Progressive Powders. — For this reason progressive 
powders have been used. A progressive powder is one 
which burns slowly at first, and. afterwards more rapidly. 

The Italian Fossano powder is an example. 

The larger grains are in the form of a cube, each com- 
posed of small dense grains united by a lighter powder. 

The grain burns at first as a cube, with a small burning 
surface, but the light powder which unites the dense grains 
soon burns out, and the cube is then broken up into a 
number of dense grains, by which the burning surface and 
the velocity of emission are greatly increased. 

The same progressive principle is found in nearly all 
powders. With molded powders and those of regular 


granulation the surface is more dense than the interior, 
owing to the method of manufacture, and hence this surface 
burns more slowly than the interior. In the molded pow- 
ders especially, the ends of the prisms next the punches 
which mold it, are most dense. Even in ordinary powders 
of irregular granulation the same principle applies. 

10. Combustion in a Close Vessel — Chemical Formula— Noble and 
Abel's Experiments. 

To determine the chemical composition of the products 
of exploded gunpowder, and the various circumstances 
attending its combustion, it is necessary to burn it in a close 
vessel, and collect the products for examination and analysis. 

Chemical Formula. — It is generally admitted that no 
chemical formula will exactly represent the results of the 
combustion of gunpowder under all circumstances, since 
these results vary, for the same powder, with the conditions 
under which it is fired. 

The formula generally adopted is 

4KNO, + C 4 + S = K,CO, + K,S0 4 + N. + 2CO, + CO. 

According to this formula we should have for the solids 
and gases of the exploded powder the following percentages 
by weight : 

K,CO, = 28.53 ) 
K a SO, - 3^96 L Solids# 

64.49 ) 

N, = 11.56 

2CO, = 18.17 

CO= 5.78 



It will be seen later that the percentage of solids is less, 
and of gases greater, than the above, and also that the actual 
constituents of both solid and gaseous products are different. 

Noble and Abel's Experiments. — Apparatus and 
Methods. — Numerous experiments have been made by Count 
Rumford (1792), Bunsen and Schischkoff (1859), an d by 


Rodman (1863), upon the composition of the products of 
fired gunpowder, the pressure produced by the gases, etc. ; 
and while many of them are valuable, their results are not 
strictly accurate, owing to defective apparatus and other 

Captain Noble of the English Army, and Sir F. Abel, a 
chemist of the British War Department, made a series of 
experiments in 1874 and a second series in 1880, which are 
accepted as authoritative on this subject. 

Apparatus.— The apparatus (see Fig. 6) was a strong steel 
vessel of the shape shown, capable of resisting very high 

IEE=? & 

Fig. 6. 

pressures. The charge of powder was introduced into the 
vessel through an opening a, which was then closed with a 
tapering screw-plug. Besides this screw-plug there was 
another, c, carrying a crusher-gauge d for measuring press- 
ures, and a third opening, e, was for the purpose of drawing 
off the gases for analysis. The charge was fired by elec- 

Methods. — Different powders were used in these experi- 
ments, and for each kind of powder a series of experiments 
was made. The volume of the explosion-chamber being 
constant, the quantity of powder in each experiment was 
varied, starting with a very small charge and proceeding 
till the chamber was filled. The maximum charge was 


2.2 pounds (i kilogram). The results of all the experiments 
were compared in order to deduce the general laws pertain- 
ing to all the powders, and the variations due to particular 
kinds of powder, form of grain, density, etc. 

11. Density of Loading — Object of Experiments. 

Density of Loading. — It is evident that the amount of 
powder fired in a given volume must greatly affect the re- 
sulting pressures. 

It is necessary, therefore, to determine accurately the 
relation between this quantity and the space in which it is 
fired. If gunpowder were always of the same density, and 
■of the same gravimetric density, we could compare the 
volume of the powder with that of the space containing it. 
But we, know that both density and gravimetric density 
vary, and hence if a vessel were one half full of two different 
kinds of powder, while the volume of powder in the two 
•cases would be the same, the actual weights would be 
different. By referring to gravimetric density, we see that 
the weights of equal volumes of powder and water are 
very nearly equal ; hence we compare the weight of the 
powder fired with that of a volume of water which will fill 
the chamber in which the charge is fired. 

This is called " density of loading," and is a very impor- 
tant ratio, which is constantly used in discussing the action of 
;gunpowder in guns or in any closed vessel. It may be de- 
fined as " the ratio of the weight of the charge of powder 
to that weight of water, at its maximum density, which will 
completely fill the volume in which the charge is fired." 

To determine an, expression for it, let 

A = the density of loading ; 
(S = the weight of the powder in pounds ; 
C = the volume in which the powder is fired in cubic 
One cubic foot of water weighs 62.425 lbs.: hence one 
pound of water occupies 

■7-1- — = 27.68 cubic inches. 
62.425 ' 


The number of pounds of water that will fill the volume 
C is 


and by definition 

A _ & _ 27.68a? (2I) 

C C K ' 


French Measure of Density of Loading. — In the metric 
system the weight of the charge is expressed in kilograms, 
and the volume of the chamber in litres or cubic deci- 

Since a litre of water weighs one kilogram, the volume 
of the chamber in litres expresses at once the weight in kilo- 
grams of the water which would fill it, and hence the 
density of loading is obtained simply by dividing the weight 
of the charge by the volume of the chamber. Therefore 


A = ~c ( 22 > 

Object of Experiments. — The object of the experi- 
ments was : 

1. To determine the nature and composition of the pro- 
ducts of combustion. 

2. The effect of varying the size of the grain, and the 
density and composition of the powder. 

3. The amount of heat generated. 

4. The volume of the permanent gases. 

5. The maximum pressure exerted by the gases, and the 
laws of its variation -, and from the data thus obtained to 
calculate the effect in the bore of a gun. 

12. Results — Nature and Composition of Products. 

Nature of Products.— In these experiments, for each, 
kind of powder the density of loading was varied by varying 
the weight of the charge, starting with a density of 0.05, and 


increasing by constant increments up to a density i.oo. For 
the latter density the vessel was completely filled with the 
powders used. The products were found to consist of per- 
manent gases and solids. Noble and Abel supposed the 
solid products to be liquid at the temperature of explosion, 
and to be diffused in a finely divided state throughout the 
gases. When the explosion chamber was opened after the 
combustion of the charge, the residue was found collected 
at the bottom in a solid form. The mass was compact and 
hard, and of an olive-green color, changing to black on ex- 
posure to the air. The volume of this residue when cold was 
about 0.3 the original volume of the powder. 

To ascertain the condition of the residue immediately 
after the explosion, the following method was adopted. 

One minute after the explosion, the vessel was inclined 
quickly at an angle of 45". It remained in this position 45 
seconds, and was then returned to its original position. 
When the vessel was opened, the solid products were 
found to be inclined to the walls at an angle of 45°. 

From this it follows that one minute after the explosion 
the solid residue was in a liquid state, and 45 seconds after 
this it had become solid. Moreover, a slight crust adher- 
ing to the walls, and which had been partially broken by 
the liquid when it took up its inclined position, showed 
that the solidification had begun one minute after the explo- 

The effect of high temperature on the solid residue was 
tested as follows. It was exposed to a temperature of 
1700 C. in a Siemens furnace. At first a slight efferves- 
cence appeared, which disappeared immediately. At the 
end of the experiment, a slight volatilization was visible. 
When the crucibles containing the residue were removed 
from the furnace, and allowed to cool, the increase in volume 
of the solid products, as determined by marks left on the 
walls of the crucibles, was about 78 per cent. 

Composition. — This was determined by chemical an- 
alysis, and was found to be as follows for pebble powder. 
The results differed slightly for different powders, and are 
the percentages by weight. 



K,CO, = 33 

K a SO.= 7 

K,S = io 

S= 4 

Various = 2 


CO, = 27 
CO = 5 

N = 11 
Various = 1 



- Gases. 

That is, 100 pounds of pebble powder, when fired, will 
give 56 pounds of solid residue and 44 pounds of gases. 
A mean of the results from all the powders gave 57 pounds 
solids and 43 pounds gases. That is, the solid residue is 57 
per cent and the gases 43 per cent of the original weight of 
the charge. The theoretical reaction gives 64.49 P e , r cen t 
solids, and 35.51 gases. 

13. Results — Effect of Variations in Powder — Amount of Heat 
Generated — Volume of Permanent Gases. 

Variations.— Slight variations in size and density of 
grain were found to have very little effect upon the composi- 
tion of the products of combustion, and no effect whatever 
upon the pressures. Hence the pressure in a closed vessel 
is independent of the size, form, and density of the grain, 
and depends only on the density of loading or the quantity 
of powder. The case is very different for a gun, as will be 
seen later. 

Amount of Heat. — The amount of heat generated by 
the explosion was measured by immersing the steel ex- 
plosion-vessel after discharge in a calorimeter containing a 
given quantity of water at a known temperature, and noting 
the rise of temperature of the water. 

The mean result obtained was that 705 units of heat were 
given off per unit weight of powder burned. Now if the 
mean specific heat of the products of explosion were accu- 


rately known, the temperature of these products at explo- 
sion could be determined by the formula 


in which Q is the quantity of heat, and c the mean specific 
heat at constant volume. But this value of c is not known. 
It is known that the specific heat of the solid products 
increases with the temperature, "but the law of increase is 
unknown. Bunsen and Schischkoff found from their experi- 
ments a value for c = 0.185. From this we should have 

™ 705 

T = —~ = 3811°, 
0.185 ° ' 


T % = T+273 = 381 1 + 273 = 4084° C. 

Noble and Abel believed this value to be much too large, 
for the following reasons : 

1. The specific heat of the solid products increases with 
the temperature, hence 0.185 is too small. 

2. The heat measured by the calorimeter includes all 
the heat absorbed by the explosion-vessel, as well as that of 
the gaseous products. The heat absorbed by the vessel is 
taken from the products of explosion, and hence lowers the 
temperature; therefore 705 is practically too large. 

3. A piece of platinum wire was enclosed in the explo- 
sion-chamber, and when the chamber was opened after 
explosion the platinum showed only slight signs of fusion. 
As this metal fuses completely at 2000 C, it was thought 
that if anything approaching a temperature of 4000 C. had 
been attained the metal would have been entirely fused. 
The temperature of explosion was therefore obtained by 
calculation, as will be explained. 

Volume of Permanent Gases. — This was determined 
by collecting the gases in a gasometer, and observing their 
volume at the ordinary atmospheric temperature and press- 
ure, and afterwards reducing this volume to zero centigrade. 

For the purpose of comparing the volumes of different 


gases the " specific volume " of each is used. For ordinary 
gases this is the volume occupied by a unit weight of the gas 
at zero C. and under atmospheric pressure. For gunpowder, 
it is the volume occupied by the gas from unit weight of powder 
at the above temperature and pressure, and was found to be 
280 times the original volume of the powder. That is, the gas 
from 1 kilogram of powder occupies at zero Centigrade and 
under atmosphericpressure a volume of 280 cubic decimetres. 

14. Results — Pressure of Gases — Formula. 

Pressure. — For each kind of powder the pressure was 
measured with the Noble crusher-gauge, for all densities of 
loading from 0.05 to 1.00. The results were plotted; the 
abscissas being the densities of loading, and the ordinates the 
"corresponding pressures. The resulting curve gave the law 
connecting abscissas and ordinates. It was then necessary to 
deduce the equation of this curve so as to express analyti- 
cally the law connecting density of loading and pressure, 
and afterwards to compare the results calculated by this 
formula with those obtained by experiment. 

Formula. — To deduce the formula we proceed as follows: 
The experiments had shown that the products of explosion 
were partly solid and partly gaseous. Hence for a given 
volume of explosion-chamber, it is evident that the volume 
occupied by the gases at the moment of explosion is equal to 
the total volume of the chamber minus the volume occupied 
by the solid products. We can then calculate the pressure 
due to this volume by Mariotte's and Gay-Lussac's laws. 

Let T, be the absolute temperature of the products at 
the moment of explosion ; 

T, the actual temperature of these products ; 

P, the pressure in kilograms per square decimetre on 
the walls of the chamber at the same instant ; 

/„ , the normal atmospheric pressure (103.33 kilograms 
per square decimetre) ; 

V, the volume in cubic decimetres actually occupied 
by the gases at the moment of explosion, corre- 
sponding to the pressure P\ 


V„ , the volume in cubic decimetres occupied by the 
same gases at zero Centigrade and at /„ pressure ; 

w, the weight of the charge in kilograms ; 

v,, the specific volume of the gases ; 

a, the volume occupied by the solid residue of i 
kilogram of powder at the temperature of explo- 
sion ; 

C, the volume of the explosion-chamber in cubic 
Then we have (Michie, equation 823), from Mariotte's 
and Gay-Lussac's laws, 

w=Ar.(2i±2) (23 > 


273+^= T t ; 

PV p.V. 


T. --273' < 24 > 

*=iP < 2 *> 


V„ = wv t (26) 


' = ^?*£ <■» 



= constant =/. (28) 

273 J v ' 

P=fy (*9> 

Now V, the volume actually occupied by the gases, is the 
difference between the volume of the chamber and that of 
the solid residue. The volume of the solid residue is 

a co. 


and hence 

V= C— aw (3°) 

The expression for density of loading is (see 22) 
Substituting this value of C in (30), we have 

and this value of V in (29) gives 

r £ 
I — a A 

p=aA-a (SO 

the equation required. 

15. Discussion of Formula (31). 

To compare the results of this formula with those ob- 
tained by experiment it is necessary to know a and/. These 
can be calculated by equation (31) by taking from the ex- 
periments two values of A and the two corresponding values 
of P, and substituting in (31). We will thus have two equa- 
tions containing the two unknown quantities a and f from 
which they may be determined. In this manner Noble and 
Abel found for these constants the following values : 

/ = 291200 kil. per sq. dee. = 18.49 tons per sq. inch. 
a = 0.57. 

Taking Noble and Abel's numerical values, we have for 
the French units 

or for English units 

p= 2 21 2COA 

P= l849J . . . /„) 

1 <— 0.57J .... v^J/ 

This value 6f a means that when the volume of the 
charge is 1 cubic decimetre the volume of the solid prod' 
nets is 0.57 cubic decimetre. 


Referring to equation (4), it is seen that the volume of 
the solid residue after explosion is nearly equal to that of 
the solid powder in the charge before explosion. 

If the charge is in kilograms, the volume of the solid 
products is obtained by multiplying the number of kilo- 
grams by 0.57. If the charge is in pounds, the volume of 
the solid products is obtained by multiplying the number 
of pounds by 27.68 and this by 0.57, or 

Vol. of solid products = No. lbs. X 27.68 X 0.57 ; 

= No. lbs. X 1577- 

When the chamber is full of powder the density of 
loading for the powders used by Noble and Abel is 1.00. 

In this case, since no more powder can be introduced, 
we should get the greatest possible pressure which gun- 
powder will give. This is sometimes called the " absolute 
pressure." Its value is by (33), for A = 1, 

P= 43 tons per square inch. 

16. " Force" of Powder — Temperature of Explosion. 
FORCE. — Assume equation (31), 

If in this equation we make 

r=rs = I ' (34) 

we have 

P = f. (34*) 

From (34) we have 

* = TT-a (35) 

Comparing this with the general expression for density, 
Of loading, 

A ™ 


we see that when the weight of the powder is unity, and 
the volume of the chamber in which it is fired is (i + a), we 
have, from (34a), 


The quantity represented by / in these equations is 
'see 28) 

f _ A v o T , 

7 273 ' 

and is constant. This value of /is called the " force" of the 
powder, and from (34a) and (35) it may be defined as "the 
pressure per unit of surface exerted by the gases from unit 
weight of powder, the gases occupying at the temperature 
of explosion a volume equal to unity." The volume of the 
chamber is 1 + <*> an d a is the portion occupied by the solid 
^products. The value of / as determined by Noble and 
Abel has been given. 

This value of / is uncertain, and therefore it admits of 
being modified to account for various resistances in a gun 
which cannot be readily calculated. 

It is found also that the values of/ for different powders 
are nearly the same. This arises from the fact that the 
quantity of heat of a powder varies approximately inversely 
as the specific volume of the gas ; and by (28) the product 
of these two quantities measures the force of the powder. 

Temperature of Explosion. — Assume, (28), 

from which 

We have found 

r.=l$m (36) 

/= 291200 

v, = 280 ; 
A = 103.33. 


Substituting in (36), we have 



= 29I2QOX273 = o C 


T =2748- 273 = 2475° C. 

These values agree well with the melting-point of plati- 
num, and could be accepted if there were no doubt about 
the value of / 


17. Action of Gunpowder in a Gun. 

Suppose we have a charge of powder which completely 
fills the chamber of a gun, the density of loading being 
unity. If this charge be completely burned before the pro- 
jectile moves, we obtain, by equation (33), 

P = 43 tons per square inch. 

0' 0" A B 

Fig. 7. 

In Fig. 7 let be the position of the base of the pro- 
jectile before firing, OX the axis of the bore, and OP the 
axis of pressures. Lay off OP = 43 tons, and we have the 
pressure corresponding to the instantaneous combustion of 


the charge. From this point P the gas will expand accord- 
ing to the hypothesis adopted, and, acting on the projectile, 
will cause it to move rapidly down the bore, the ordinates 
of the curve Px representing the pressures at correspond- 
ing abscissas of travel. The equation of this curve will be 
deduced later. 

Error in Supposition. -~\X. is evident that the assumption 
that all the powder is consumed before the projectile moves 
cannot be true in practice. As soon as the pressure rises 
high enough to overcome the resistance of the projectile 
and gun to motion, they will both move in opposite direc- 
tions ; but for the present we will consider the motion of 
the projectile alone. 

Quick-burning Powder. — Take a small-grained powder of 
cubical form. The time of combustion of this powder is 
small, and its velocity of emission at first great, as has been 
shown. Let OP' represent the pressure which is sufficient 
to start the projectile, and suppose the powder is all burned 
when the projectile reaches A: tJnder these circumstances 
the relation between the pressures and the travel of the 
projectile, or the " pressure curve," will be represented by 
a curve such as OP'P"abx. 

Slow-burning Powder. — Take the same weight of charge of 
cocoa or slow-burning powder. The time of combustion 
is comparatively great, and its velocity of emission at first 
small. Let OP' represent, as before, the pressure required 
to start the projectile, and suppose the powder all burned 
when the projectile reaches B. 

The pressure curve in this- case will be OP'P'"bx ; and 
from these curves we may deduce the following conse- 
quences : 

a. The quick curve will rise above the slow one near the 
origin, because the volume of gas given off in the same time 
is greater with the quick powder. 

b. The work done by the quick powder upon the pro- 
jectile is greater than that done by the slow powder, be- 
cause the area under the quick curve is greater than that 
under the slow one. 

c. The quick powder strains the gun more than the slow 


one, because the maximum pressure O'P" > 0"P'", and this 
maximum pressure is what determines the maximum strain. 
That part of each curve from P' to a and b, respect- 
ively, is called the combustion curve, because during this 
time the powder is still burning and giving off gas. The 
part from a and b to x is called the expansion curve, be- 
cause from these points on the gas is expanding only. 

18. Equation of Pressure Curve — Noble and Abel's Method. 

The equation of the true pressure curve is very difficult 
to deduce, since at the origin, as we have seen, gas is being 
evolved while the projectile is moving, and this renders the 
problem very complex. 

Noble and Abel deduced the equation of the curve Pabx, 
Fig. 7, under the following hypotheses : 

i. That all the powder is burned before the projectile 

2. That the solid products of combustion give off heat 
to the gases during the expansion. 

Let t, represent the specific heat of the solid products, 
supposed constant throughout the expansion, and dT„ any 
small change of temperature of the products of combustion. 

Then c,dT is the corresponding quantity of heat given 
to the gases by the solid products per unit of weight. 

Let w, represent the number of units of weight of the 
solid residue ■ then the total quantity of heat given to the 
gases by the solid residue is w.c.dT^. Let a/, be the number 
of units of weight of the gases. These gases, by hypothesis, 
receive the heat above found, and hence they receive per 
unit of weight a quantity of heat dQ equal to 

dQ=-^c 1 dT t =-{lc 1 dT t ( 37 ) 

/? being the ratio — , and the negative sign being used since 

T t is a decreasing function of Q. 

When the volume, pressure, and quantity of heat of a 
gas change at the same time, we have a general law con- 


necting them, which is expressed by the following equation 
(Michie, 832) : 

dQ = cj>dp + c t pdV t (3g) 


Ml which dQ is the elementary quantity of heat imparted to 
the gases ; 
dp and dv the elementary changes of pressure and 

volume of the gas due to dQ ; 
c t and c„ the specific heats at constant pressure 
and volume, respectively. 
Substituting in equation (38) for dQ its value given by 
(37), we have 

- fcdT, = ^c v vdp + c t pdv) (39) 

This equation contains T a and R, while the equation of 
the pressure curve should contain only/, v, and constants, 
because the pressure curve is one showing the relation be- 
tween / and v. To eliminate T, and R, assume the general 
equation (823, Michie) connecting the pressures, volumes, 
and temperatures of a gas. 

pv = RT, (40) 

Differentiating, we have 

RdT, = pdv + vdp (40') 

from which 

,~ pdv -\- vdp 

Substituting this value of dT in (39), we have 

-(#. + 0$ = (/»<• + '.) J (40") 

For small changes of pressure and volume /S, c x , c t , and c r 
are constant. Hence 


J> it p, v { , and v being* the initial and any subsequent values 
ot p and v. 


J^+7,~ k ' (42) 

we have 

'^'KT (43) 

the equation of the pressure curve. 

19. Application of Formula (43)— Work of Gunpowder in a Gun. 
Application. — Assume equation (43) 



In this equation v t is the volume occupied by the gas at 
the moment of explosion, and /,• the corresponding press- 
ure. To apply this equation to the case of a gun, the 
original volume v { occupied by the gas, is the volume of the 
chamber in which the charge is fired, minus the volume 
occupied by the liquid products of the charge. The volume 
v occupied by the gases corresponding to the pressure p 
is the total volume to which the gas has expanded, including 
that of the chamber, minus the volume occupied by the 
liquid products. 

Hence if v' denote the original volume of the chamber, 

' the density of loading being unity, av' is the volume occupied 

by the liquid residue, and v { — v' — av' = v'(i — a). Also, 

if v" represent any subsequent volume of the bore, at which 

the pressure is /, the volume actually occupied by the gas is 

v = v" — av' . 

Making these substitutions in (43 1 ), we have 

( v'{l - a)y . , 


Taking from the experiments the values of the constants, 

we have 

' pi = 43 tons per square inch ; 
«=o-57; /? = 1.2957; 

c p = 0.2324 ; c v = 0.1762 ; c, = 0.45 ; 

k' = 1.074, 
and substituting in (44), we have 

P = 43(^=^/) 1074 (4S> 

for use in practice. 

Work of Gunpowder. — The general expression for the 
work done by a gas expanding from a volume v t to a volume 
v is 

W= / pdv (46) 

Substituting for p its value from (44) and changing the 
limits to v" and v', we have 


%s v' 

F" dv" 

w=p i v>*(i-«yj^ K _ gp y - 

Integrating, we have 

, r Ar/ ,> o -<*)*' r 1 1 "1 ,.„* 

^ _/i 12 X (# - i)L[w'(i - a)]* - ' (»" - W)* - 'J^ 40 ' 
Multiply, and divide the second member by [v'(i — a)]*'- 1 .- 

w - i2x{# - 1)1* -wrurf) } ■ (49) 

12 is used to reduce to foot-tons. This is Noble and Abel's 
formula for work. 

Taking the volume corresponding to the muzzle of the 
gun, the corresponding work is obtained. If there were no* 
loss of energy due to the friction, resistance of rifling, etc., 


the work thus calculated should be equal to the energy in 
foot-tons possessed by the projectile at the muzzle, which is 

E = 

2g X 2240 ' 

■w being the weight of the projectile in pounds, and V its 
muzzle velocity in feet per second. But E is always less 
than W, owing to the above causes ; and the ratio 

is called the " factor of effect " for the particular gun and 

Knowing this factor for any given gun we can find the 
muzzle velocity for a given charge by calculating W by (49), 
multiplying it by F, and we have 

. — — = FW; 

2g X 2240 

from which 

v= ^ £ wx^_xj m ^ (5o) 

Infinite Expansion. — When the length of bore becomes 
infinite, v" in (49) is infinite, and we have 

W= P^=^L (SI) 

\2(k' — I) x 

Using the constants as given above, and substituting for 
v' its value, 27.68 cubic inches, the volume occupied by one 
pound of powder, we have 

W = 576.35 ft-tons (52) 

for the work of one pound of powder expanded to infinity, 
under Noble and Abel's hypothesis. 

20. Equation of Pressure Curve— Recent Hypothesis— Expression 
for Work under this Hypothesis. 
Equation of Pressure Curve. — In recent discussions 
JNoble and Abel's hypothesis is rejected, as it is believed that 


from the feeble absorbing power of gases generally, they re- 
ceive only a very minute quantity of the heat radiated by the 
solid products. The equation of the pressure curve Pabx y 
Fig. 7, is therefore deduced under the following hypotheses, : 

i. That all the powder is burned before the projectile 

2. That the gases expand without receiving heat from or 
giving off heat to any external source, and that the work 
done on the projectile is due to their own heat ; that is, the 
expansion is adiabatic. 

Assume the equation expressing the general law con- 
necting the heat, volume, and pressure of a gas, as before,, 
(equation 832, Michie's Mechanics), 

_ c v vdp -f c p pdv 

Since no heat is gained or lost externally, dQ = o and 
we have 


Making -£ = k and integrating between the limits p t ,p„ 
Vi and v, we have 

log f - log (!■)*, ( S3 > 


> = ><[£]* <54> 

which is the equation of the pressure curve, and differs from 
that deduced under Noble and Abel's hypothesis only in 
the value of the exponents k and k', k' being 1.074 and k, for 
powder gases, 1.30. 

Work. — To deduce the expression for work in this case,. 
we have, as before, equation (46), 



= I pdv. 


Substitute for p its value from (54), integrate, and we 

w =-i~r- k + c - (55) 

When v = v t we have W=o, and C = , ; hence 

21. Work of Gunpowder in Terms of Force and Weight of Charge 
— Expression for it in Terms of Length of Travel of Projectile. 

Work in Terms of Force and Weight. — If cS be the 
weight of the charge in kilograms, the initial volume occu- 
pied by the gas from each kilogram of powder, expressed in 
cubic decimetres, will be 


piVi^piV.w; (57) 

and from Mariotte's law we have 

p i v l = p"v" = C (a constant), 

see equation (814), Michie's Mechanics. 

Now if we make v" = 1 = one cubic decimetre, /" be- 
comes by definition the force of the powder, and hence 

Pfi>, =P" =/; 
and from (57), 


Substituting in (56) for/^,- this value, we have 

-=^l ■-£)'"'} w 

in which W is expressed in terms of the " force of the 
powder " and its weight. 

In equation (58) the force of the powder is expressed in 
kilograms per square decimetre, and the volumes in cubic 
decimetres. Hence the work W will be expressed in kilo- 


gram-decimetres. It is usual, however, to express work in 
kilogram-metres, and this is done by dividing by 10; and we 

*=W- /s 

IO Io(£ — i) 

{-©'"}•• •(») 

Work in Terms of Length of Travel of Projectile. 
— We can place this expression for work under a still more 
convenient form, as follows : 

Reduced Length of Initial Air-space. — The initial air-space 
in the powder-chamber is equal to the total volume of the 
chamber minus the volume occupied by the solid powder; 
and the reduced length of this air-space is the length of a 
cylinder whose volume is that of the initial air-space, and 
whose area of cross-section is that of the bore proper. 
To determine its value, 

let A be the density of loading ; 
£, the density of the powder ; 
w, the area of cross-section of the bore ; 
z, the reduced length of the initial air-space. 
We have 

. w „ do 

The volume occupied by the solid powder in cubic 
decimetres is 

hence the volume actually occupied by the gases, or the 
initial air-space, is 

n T , <2 do 

This volume divided by oo, the area of cross-section of 
the bore, gives z ; hence 

-(I — *\ 
w\2i sr 



Having this value for z, we have (see page 29) 

Vi = 002 ; v = oo{z -\-x) (6o«) 

x denoting the length of travel of the projectile. 
Substituting these values in (59), 

^ = 7^7)1 --tr/l • ' < 6I) 

Taking k = 1.3 and /= 291,200, we have the constants 
which enter (61), and W can be calculated for any length 
of travel x of the projectile. When x = 00 , the bore be- 
comes infinite in length, the powder expanded to infinity, 
and (61) becomes 

io(£ — 1)' 

Making o3 = 1, we have, for the work of one kilogram of 
powder expanded to infinity under the adiabatic hypothesis, 

W = 97066 kil.-metres per kilogram, 
= 142.2 ft.-tons per pound. 

Comparing this with Noble and Abel's value for the 
work of one pound, viz., 

W = 576.35 ft.-tons per pound, 

we see that the work is much less under the adiabatic 

22. Division of Work of Gunpowder — Velocity of Recoil. 

Division of Work. — Having the value of the total work 
done by gunpowder, it is required to find how much of this 
work is done upon the gun and how much upon the pro- 
jectile, and thence to deduce values for the velocity of 
recoil and of the projectile. 

In this discussion we suppose : 

1. That the gun recoils freely. 

2. That gravity and resistance of the air can be neg- 
lected in comparison with the great pressures considered. 

Then we have, from mechanics : 


i. The total energy of the system is equal to the total 
work done by the powder upon it. 

2. Since the gun and projectile move in opposite direc- 
tions with equal momenta, the sum of the quantities of 
motion of the system is zero. 

The energy of the system after the projectile has passed 
over a given path x is composed of three quantities: ist, 
the energy of the projectile ; 2d, that of the gun ; 3d, that 

of the charge. The energy of the projectile is , tn de- 
noting its mass and v its velocity of translation. To this 
should be added the energy of rotation ; but this is so small 

that it may be neglected. The energy of the gun is , 

M being the mass and v' the, velocity. 

The energy of the charge is unknown, since the velocity 
of its particles is unknown. The velocities of these par- 
ticles vary from zero, near the bottom of the bore, to v, 
that of the projectile, for those in contact with the latter, 
not taking into account irregular motions which also exist- 
Hence the mean velocity of the particles is less than 


that of the projectile. If n be the mass of the charge, £— 

would be its energy if the velocities above mentioned were 
equal ; as they are not, we represent the energy of the 

charge by ^— X 0, being a coefficient whose value is be- 
tween zero and unity. 

We have, then, as a first equation, 

2W =mv 1 +Mv" + M tf (62) 

The momenta of projectile and gun are mv and Mv'. 
As before, the quantity of motion of the charge is not 
known; but, reasoning as above, we may represent it by 
d'fiv, and its sign will be +, because, as the centre of grav- 
ity of the system is fixed, the greater part of the gaseous 
mass moves in the same direction as the projectile. The 
second equation is then 

mv 4- 6'nv — Mv' = (63} 

--',,'- (64> 


The values of 6 and 6' are found by analytical methods 
to be 

6 = h »' = * 
Velocity of Recoil.— From (63) we have 

m + B'n 

Make v= Fthe initial velocity, and we have v' = V, the 
velocity of the gun at the moment the projectile leaves the 
bore. Making 0' = i, and replacing masses by weights, we 

P + - 
V' = — p - 2 -V. (6 S > 

Experiment shows that this formula gives correct values 
for V at the instant the projectile leaves the bore, suppos- 
ing the gun to recoil freely. But this value of V does 
not represent the maximum velocity of recoil ; in fact, it 
gives only about three fourths of the maximum, since it 
applies only at the instant the projectile leaves the bore. 
For slow powders the velocity of recoil is increased, since 
the gas continues to act upon the piece after the projectile 
has left the bore. 

The subject of recoil will be further discussed under 

23. Velocity of Projectile — Passive Resistances — Limit of Length of 
Bore — Influence on Velocity and Maximum Pressures. 

Velocity of Projectile. — Substitute the value of v' 
from (64) in (62), and we have 


m -V On + i jf- 1 - 

This equation gives the velocity of the projectile as a 
function of the work of the powder. The third term in the 
denominator, being generally small, may be omitted, and 
we have 

V = J-2T- (67> 



If we have a quick powder, and suppose it all burned 
before the projectile moves, we may substitute for W in 
{67) its value from (61), which gives 

• = & jr-pLri. 

5(£ - i)(wz + 0/<) ( \2-\-xI ) 

Making x = u, the total length of travel of the projectile, 
■»" becomes the initial velocity, and we have 

V* - f & 

%^y uj \ 

For a long gun « would be large and small, and 

z -\- u 

V would become 

5(*-i)(* + ^j 

The value of / in this equation must be found by experi- 
rrient, to compensate for the erroneous assumptions made in 
deducing it. 

Passive Resistances are those due to the forcing of 
the band of the projectile into the grooves of the rifling, 
friction, etc. 

Let p denote the work done against these resistances 
•over the path x. In equation (62) this work is not ac- 
counted for, and it is therefore not exact. Introducing it 
into that equation, we have 

2(W-p) = mt? + Mv n + 6/M?; ... (69) 
and in equation (67) we have for the velocity 

m 4- 0)i 




Length of Bore. — Although the value of p is unknown, 
we can use it as follows : Differentiate (70), v, W, and p being- 

\dW-dp , x 

dv = 

v m -|- Of* 
In Fig. 8 let OX be the axis of the bore and OP that 

Fig. 8. 

of pressures. Suppose the bore divided into elementary 
lengths dx. Then, since the length multiplied by the con- 
stant area of bore is the volume, we may replace dx by dv, 
the increment of volume, as in the figure. From equation 


dW = pdv; 

and each of the small areas bounded by the pressure curve, 
the ordinates, and dv will be a value of d W. In the same 

dp = Kdv, 

K being a constant and equal to the constant pressure be- 
tween projectile and rifling multiplied by the coefficient of 
friction. Since K and dv are both constant, the values of 
dp will all be equal, and they are bounded by the straight 
line KK', the ordinates, and the axis of X. 

As the projectile moves from toward X, the increment 


of the work due to friction remains constant, while dW de- 
creases and tends towards zero, since / constantly decreases. 
There is some point, then, such as m, where 


or dv = o. This value of X will be greater for a slow 
powder than for a quick one, because, as we have seen, for 
equal charges the slow powder gives a less maximum pressure, 
and hence we can use larger charges of slow powder without 
overstraining the gun ; and as these large charges give off 
more gas, the pressure is kept up better along the bore than 
with the quick powder, or the values of / are greater along 
the bore, dp being independent of the nature of the powder. 
When the point m is reached where dv = o, or the velocity 
of the projectile ceases to increase, the limit of length is 

With small arms this limit is attained more nearly than 
with cannon ; and the above reasoning shows that slow 
powder requires longer bores than quick powder. 

Influence on Velocity and Maximum Pressure. — 
Equation (70) shows that the passive resistances decrease the 
initial velocity of the projectile ; but this is not always the 
case. Certain passive resistances, such as the resistance of 
the rifling, produce at first a more rapid combustion of the 
powder on account of the' rise in pressure due to the delay 
of the projectile in moving off. Hence the powder acts as 
a quicker powder, the work done by it over a given path is 
increased, and this increase of work may more than com- 
pensate for the resistance. It follows as a consequence 
that the maximum pressure on the gun is increased. An 
accidental resistance, such as wedging of the projectile, 
may cause a great increase in pressure, and, if it cannot be 
overcome, may burst the gun. 

24. Sarrau's Formulas— General Equation of Motion of Projectile 
in Bore. 
The formulas deduced above furnish approximations to 
the initial velocity of the projectile, but are not exact for 
many reasons. Among these are : 


ist. The powder is supposed to be all burned before the 
projectile moves. This is known to be incorrect. 

2d. No account is taken of the passive resistances. 

3d. The kind of powder and the calibre of the gun are 
not considered. 

For these reasons it was customary to use empirical for- 
mulas. These formulas gave good results so long as the 
conditions under which they were deduced were not de- 
parted from, but they were limited in their applications and 
could not be generally used. 

To obviate these difficulties, the subject has been dis- 
cussed by M. Emile Sarrau, a distinguished French engineer 
of powders, etc. In his discussion the following hypotheses 
are adopted : 

1. The inflammation of the charge is instantaneous. 

2. The gases expand adiabatically. 

3. The powder is not all burned before the projectile 

Equation of Motion. — At the end of any time t let 

q be the weight of powder burned ; 
x, the length of bore passed over by the projectile ; 
/, , the mean pressure ; 

v x , the volume of the bore in rear of the base of the pro- 
jectile, minus the volume occupied by the solid 
residue of the powder ; 
v, the velocity of the projectile. 

The gas which is formed at the time / expands adiabati- 
cally, and we have, for any time t' after t (see equation 54), 

/V» =/,»,* (72) 

p' and v' being the mean pressure and volume at the time 
/', and k the ratio of specific heats. 

The total quantity of work done up to the time /' is, from 


W= /' fi'dv'. 



Substitute for /' its value from (72), integrate, and we 

W=-£^-v»-* + C. (73) 

To find the value of the constant : When t' = /, we have 
v' = v t ; and if we consider the energy of the projectile 
alone, W = \mv'; hence 

c=w + £!!!_ 

and consequently 

w =-{zh*' 1 -*+*«*+jgt- 1 . . . (74) 

If we now suppose the bore to be infinite in length, v' 
becomes infinite, and W becomes, from (61), 

W= fq ■ 

\o(k - 1) ' 
and since k > 1, 

P^ v 

i_ 7 /j - k 

becomes zero. Hence 

io(k — 1) a * k—i ^ /5 ' 

25. Transformation of Equation (75).— Errors in its- Deduction and 
their Correction. 
Transformation.— Equation (75) is transformed as fol- 
lows : Make 


v = dT' 

v, = w(z + x) ; (see equation 600 ;) 
p ^ = m ~dF- • (75«> 

This last equation expresses the fact that the total press- 
ure on the projectile,/^, is equal to the accelerating force. 


While this is not exactly true, it is sufficiently accurate, 
and can be corrected for, as will be explained. 

Making these substitutions in equation (75) and including 
the constant 10 in /, which is equivalent to changing the 
unit in which the force of the powder is expressed, we have 

fq mldx\' , d 7 x z 4- x 

Errors and Corrections. — In deducing this equation 
certain errors have been made. These are : 

1. The total work which a weight of powder is capable 

of doing, when expanded to infinity, is not equal to -—^- — T 

because part of the heat is absorbed by the walls of the 
bore, and no allowance has been made for this loss. 

On the contrary, we have supposed an adiabatic expan- 
sion without gain or loss of heat. Hence -. is too large 

rZ ~~ I 

and must be diminished. 

2. At any time t the work of expansion is not equal to 
$mv\ but is equal to the total energy of the system, includ- 
ing gun, projectile, charge, and gun-carriage. 

To correct for this we must increase the term i^(^r) . 


3. We have assumed p,a> = m—jr, or that the total! press"- 

ure on the projectile is equal to the accelerating force. 

This is not correct, because the force />,&> not only pro- 
duces acceleration of the projectile, but overcomes the 
passive resistances, such as forcing of the band, friction, etc. 

Hence, in order to make p^o = fn—j^-, we must increase 

m — - 

Instead of correcting each term of equation (j6) as in- 
dicated, we can apply such a correction to the first member 
as will make it a true equation. The numerical value of f 
is uncertain, and we may therefore apply all the corrections. 


to this quantity, and / then becomes a numerical coefficient 
"whose value must be determined by experiment. 

26. Deduction of Final Equation of Motion of Projectile in Bore. 

Value of q. — The method of determining the value of/ 
iin equation (76) has been explained. It is necessary now to 
find the value of q, the quantity of powder burned at the 
end of any time t. 

The proportional part of powder burned in air at any 
time / is given by the general expression, (12), 

#i) = f(i -*£ + /£ + etc.). • • • (77) 

By multiplying this expression by the volume of the 
grain or charge we obtain the volume burned (see equation 
(16) ) ; and multiplying the same expression by the weight, 
we have the weight burned at any time. 

Hence, 60 being the weight of the charge, we have 

<? = <30(O (78) 

But the expression (tj) applies to the burning of a gram 
or charge in air. In a gun, the pressure varies and is much 
greater than in air, and hence the velocity of combustion 
varies and is much greater, as has been shown; and this 
variation of velocity is expressed by Sarrau's formula 
already given (equation 11), 

*•&)*: (79) 


and the expression for <p(t) must be modified accordingly. 

Spherical Grain. — Take the simplest case, that of a spheri- 
cal grain. When burning in air, we have found for the vol- 
ume burned at any time t, equation (13), 

i Ttr 3 - &7c(r - vt)\ 

Since v is no longer constant, owing to the variation of 
pressure in the gun„ the space burned in the time dt is vdt ; 


and in the time t it is / vdt, instead of vt, as in the case of 

constant pressure. The above expression for the volume 
of powder burned in the case of a spherical grain under 
varying pressure becomes, then, 

%nr % - %n[r -J vdt); (80) 

and the value, of <p(t) in equation (14) becomes 

$(t) = 1 - (1 - -f'vdt} (81) 

If in this equation we substitute for v its value from (79), 
we have 

*>=-[-?j(W- • • • <*> 


r = -, 

the time of combustion of the grain in air under the normal 
pressure, and 

,_i = I. 
r r 

Substituting in (82), we have 

Comparing this value of <p(t) with that for uniform 
pressure, which is, equation (17), 

0(7) = 1 - (1 - LJ, (84) 

we see that the only difference is the substitution of 

for /. 



Following the same method for other forms of grain, the 
same results will be obtained. Hence we conclude that if 
the combustion of powder under constant pressure is repre- 
sented by 

*« = ^(i-Af + /£+etc.), 
the combustion under variable pressure will be represented 

*»=^H-^)'* +ete ]-- <8S> 

Final Equation. — In equation (85) make 

p —p t the mean pressure at the time /. 

/,<» = m-~ (see equation (75«)). 



and we have for the value of the term / ( — ) dt, 

m*=wm^ ■ ■■<*» 

and substituting this value in (85), we have 

and for the value of q, 

q = <3<p(i) = <3 X 2d member of equation (87). . (88) 
In equation (76) make 

and it becomes 


Substituting in this equation the value of q from (88), we 
have the final equation desired, which is 

27. Integration of Equation (90) — Practical Formulas for Velocity 
and Pressure — Values of A and B — Characteristics a and /3. 

Integration. — Equation (90) must be integrated before 
it can be used practically. Sarrau has done this by the use 
of auxiliary functions which are numerical and independent 
of the variable elements of fire. As a final result of his 
process, the general values for velocity and pressure are 
expressed in the form of definite series, which are very con- 
vergent. On this account it is necessary to consider only 
two terms of the series in the expression for the velocity, 
and only one term in the expression for the pressure. 

Binomial Formula for Velocity.— Considering the 
two terms of the series, Sarrau's formula for velocity is ex- 
pressed as follows. It is called the binomial formula for 
velocities, and is the result of the integration of equation 
<9o) : 

, = ^«(^J[r-V^]; • . • (91) 

in which v is the velocity of the projectile at the point u, 
and becomes the muzzle velocity when u is 
equal to the total length of travel of the pro- 
jectile in the bore ; 

«, the length of bore passed over by the base of 
the projectile in inches, measured from the 
position occupied by it before firing. In 
equation (90) this length is denoted by x, and 
is changed to u in formula (91) ; 
c, the calibre or diameter of the bore in inches ; 

/, the weight of the projectile in pounds ; 

<3, the weight of the charge of powder in pounds ; 

A, the density of loading ; 


a and /J, two coefficients depending on the nature of the 
powder used, and called the "characteristics" 
of the powder ; 

A and B, two numerical coefficients which are independ- 
ent of the elements of fire. 

The values of a and ft are 

« = (*)' ' = £ ^ 

in which /is the force of the powder; 

a and A, coefficients depending on the form of the grain 
of powder, and whose values for the different 
iorms of grain have been given ; 
r, the total time of burning of the grain in air. 

Formula for Maximum Pressure on Base of Pro- 
jectile. — In the same way, as the result of integration, the 
expression for the maximum pressure on the base of the 
projectile is 

P=K*A& (93) 

in which the quantities are the same as before, and K is a 
constant whose value is to be determined as will be ex- 

Values of A and B. — If for a given powder we know the 
values of a and ft, we can fire this powder from two differ- 
ent guns, and measure the resulting initial velocities. This 
will give v. The values of c, tt, and p are known for the 
two guns, and the values of c3 and A also, and, having two 
equations containing A and B, they can be calculated. But 
it is difficult to find exact values for a and ft, since they de- 
fend on / and r, equation (92), and the values of these quan- 
tities are uncertain. To avoid this difficulty, Sarrau adopts 
a particular powder which he calls a type powder, and 
assumes for it the values /= 1, r = 1. 

The values of a and A for the type powder are calculated 
as explained previously. Hence all the quantities in (91)' 
are known except A and B, and they can now be calculated- 


Since A and B are constants to be determined experimen- 
tally, whatever errors we make in assuming the values of / 
and r will be corrected for in the values of A and B as found 
by experiment ; and since these values of A and B are inde- 
pendent of all the elements of fire, they will be true for all 
powders and all guns. A and B are found by experiment be- 
cause they depend on v, which is determined by experiment. 

In this way Sarrau found the values of A and B to be 

log A = 2.56635 ; 
log B = 2.30964. 

Characteristics a and /?.— Having the values of A and 
B in (91), we must know the characteristics a and /3 for any 
powder before we can apply the formula to this powder. 
The values of a and /? depend on /, a, X, and r (see (92) ). 
a and A. can be calculated, as before explained, for an)' grain 
of ordinary shape, and their values for most service forms 
have been'given. The value of /is uncertain, and therefore 
for simplicity Sarrau assumes ./"= 1 for all powders, the 
same as for the standard powder. 

We have seen that/" is practically constant for all pow- 
ders, and hence the above assumption may be made. The 
value of r cannot be accurately determined except by the 
use of a formula not yet deduced, and hence the method of 
determining it will be explained later. 

28. Maximum Pressure on Breech of Gun — Value of K. 

Maximum Pressure. — Equation (93) gives the maximum 
pressure on the base of the projectile, and in order to use 
it K must be known. If we could measure accurately the 
pressure on the base of the projectile, the value of K could 
be found by firing a shot from a gun, since all the quantities 
except K in (93) would be known, and hence it could be 
determined. But this pressure cannot be accurately meas- 
ured, and hence we determine first the maximum pressure 
on the breech. 

To do this assume equation (64) : 

, m -\- 6' 11 

v = — mt — v - 


Differentiate with respect to t : 

dv' _^m-\- &' ' )* dv 

dt M dt 


Multiply both members by — , oo being the area of cross- 

section of the bore : 

: *f( 1 + «KZ) ( 95 ) 

w dt 

Now denoting by P the maximum pressure per unit of 
surface on the bottom of the bore, and by P the correspond- 
ing pressure on the base of the projectile, we have 

Pea = m—r ; 


and substituting in (95), 

P ' = P i 1 + 6 'i) ( 97) 

Substituting weights for masses, and for 6' its value i, 

^=4+|) (98) 

This equation does not give true values for P a , since in 
placing the total pressure equal to the accelerating force, 
equation (96), we have evidently neglected the force neces- 
sary to overcome the passive resistances. Sarrau has there- 
ifore adopted, as more nearly agreeing with experiment, the 
following formula : 

p -=K'+iji to) 


Substituting for Pin (99) its value from (93), we have 

P. = K(,+lj) a .JJfi.. . . . (loo) 


('+ff)=MD' coo 

we have 

P. = KK>\*f*J& ( 102 ) 


KK> = K 

r = h 

-which is justified by experiment, w have finally, for the 
pressure on the breech, 

or reducing, 

P = Kt *A*± (103) 

Since we can measure very accurately the pressure on 
the breech of a gun, we fire with a given powder, measure 
this pressure, substitute it for P in (103), and, as all the 
other quantities except K a are known, we thus obtain its 
value, which is 

log K t = 4.25092. 

Value of K in (93). — Having the value of/',, we substi- 
tute it in (99) and find the corresponding value of P. This 
value of P in (93), together with the known values of the 
other quantities, will give K, whose value is 

log ^=3.96197. 


Collecting the pressure formulas for convenience, we 

P — Ko?Al—L-, on base of projectile 

P t = K^A*^-, on breech of gun. 

log J ST=3-9 6l 97; 
log K = 4.25092. 

29. Theoretical Maximum Velocity— Time of Burning Correspond- 
ing to the Maximum Velocity. 

Maximum Velocity. — Assuming the binomial formula 
for velocity, and replacing a and /3 in it by their values, 
equation (92), 


P = -, 


we have 

•='®to$T-4^- • • <-> 

If in this equation we make v and r the only variables, it 
can be shown by the usual rules of calculus that v will have 
a maximum value for a particular value of r. That is, as 
r decreases in value, v will increase till it reaches a maxi- 

But this ought not to be the case, because, theoretically, 
as r decreases, or the powder becomes more quick, v should 
increase ; and this increase should continue up to the limit 
where the combustion is practically instantaneous and r = o. 

Formula (104) gives this maximum value for v because it 
is not absolutely correct, but only approximate. It will be 
remembered that in its deduction it was stated that the 
value for v was expressed in the form of a series, of which 
the first two terms only were retained. But the function 
represented by this series may go on increasing when r 
decreases below the value which makes the sum of the first 
two terms a maximum, provided the sum of the other terms 
goes on increasing. 


The value of r corresponding to the maximum of the 
first two terms is nevertheless important, because it marks 
the limit below which a decrease in r gives only a slight 
increase in the velocity. It is not advisable to pass below 

this value of r in practice, because a — (— ] enters the 

pressure formulas (93) and (103) to the second power, and 
r being in the denominator of the value of a, a small de- 
crease in r causes a rapid increase in the value of a, and 
hence in that of the maximum pressure, while the gain in 
velocity, as shown by the previous discussion, is very small. 

Value of r corresponding to the Maximum Value 
OF v. — The particular value of r which corresponds to this 
maximum value of v is called the " time of the maximum." 

Differentiating equation (104) with respect to r, placing 

-r- — o, and solving for r, we have, calling the resulting 
value r lf 

r,= lBT^L (lo5) 

This shows that for a given form of grain, the value of r, 
or the time of the maximum, depends, on the calibre, weight 
of projectile, and length of travel, and is independent of the 
charge of powder and density of loading. 

For the same powder, the weight of the projectile p is 
proportional to the cube of the calibre, the length of travel 
u to the first power of the calibre, and hence, since 3-5A. is 
constant, we may write, from (105), 

r 1 ^r- 1 L =f{c), (106) 

or the time of the maximum is proportional to the calibre of 
the gun ; that is, to obtain the greatest velocity, the time of 
burning should increase as Lie calibre of the gun increases, 
or large-grain powder should be used in large guns, which 
proves the principle enunciated by Rodman. 


30. Modulus of Quickness — Value of Modulus — Velocity and Pres- 
sure as Functions of this Modulus. 

Modulus of Quickness. — Powders are called "quick" 
or " slow " depending upon their action in a given gun. A 
given powder may be "quick" when used in one gun and 
"slow" when used in another. For example, the I. K. pow- 
der which is used in the 3.20-inch field-guns is " quick " when 
used in the 8-inch rifle, and " slow " when used in the Spring- 
field rifle. From equation (105) we can calculate the value of 
r, , or the time of the maximum, for any gun and powder. 

A powder whose time of combustion is much greater 
than this is called a slow powder for this gun, and one whose 
time of combustion is nearly equal to this is called a quick 
powder for the same gun. 

Also two powders fired in different guns are considered 
equal, as regards their quickness, if their times of combus- 
tion are proportional to the " times of the maximum" of the 
two guns considered. Hence, if we make 

x = i (107) 

and call this ratio x the " modulus of quickness " of the 
powder, we can say that the quickness of a powder is meas- 
ured by its modulus. 

On this basis Sarrau classifies powders as follows : 

x = 1.0, very quick powder; 
x = 0.9, quick powder ; 
x = 0.8, medium powder ; 
x = 0.7, slow powder ; 
x = 0.6, very slow powder. 

Value for Modulus.— We have, from (107), 

x = \ 



Substitute for r, its value from (105), and we have 

and since from (92) 

X = 


c ' 

/» = 

: r' 

X = 

= 3*A 


we have 

( *»\i 


Velocity as a Function of the Modulus x. — To ex- 
press the velocity as a function of the modulus, we have 
for the subtractive term of the binomial formula (104) from 
' (107a), 

*{puf _x 

and for r from the same equation, 


x = 



Substituting the value — for the subtractive term, and for r 

its value above, in the factor ( — ) in the binomial formula, 
we have 

w = ^(3-S)-*(^)*«3i^*«*«*^-***[3-*]. . (109) 


i**[3 - ■*] = /(*)» ( I0 9 a ) 

we have 

<52 text-book of ordnance and gunnery. 

Maximum Pressure as a Function of the Modulus 
x. — By a similar process the pressures on the base of the pro- 
jectile and on the breech may be expressed in terms of x. 

For the maximum pressure on the base of the projectile 
we have 

*=*wr-££- ('■» 

and for that on the breech 

P.=*.(3*)-4(f)'^ . . . (.») 

31. Limit of Use of Binomial Formula. 

It has been shown that v in formula (91) becomes a max- 
imum when t decreases to a particular value r, , and also 
that v should not be a maximum for this particular value of 
t, but should increase continuously as r decreases. 

It is also evident from (107) that when r becomes r l , x, 
the modulus, becomes unity, or & = 1. That is, the velocity 
is a maximum by formula (91) when x = 1. 

The value of x from (108) is 

* = 3^ (,13) 

and the subtractive term of the binomial formula is 

BP— , (1 14) 

which is % of x. Hence when v becomes a maximum in (91), 
x becomes unity, and the subtractive term of (91) becomes \. 
This value for the subtractive term would then mark 
the limit of the use of the binomial formula, were it not for 
the fact that as a function approaches its maximum it 
changes its value very slowly, and hence before we reach 
the value x = 1, the binomial formula will cease to give cor- 
rect results. For this reason Sarrau adopts the value x = T «j- 
for the particular value of the modulus at which it is best to 
cease the use of formula (91). 


When x = T 9 T , the subtractive term, being \ of x, will be 
£ of -j^- = 0.273. Hence we have for determining the limit 
of the use of the binomial formula the rule : Calculate the 
value of the subtractive term in the binomial formula ; if it 
is greater than 0.273, the binomial formula is not applicable ; 
if less than 0.273, it is applicable ; or 

Bfl > 0.273, do not use binomial formula ; 

Bfi < 0.273, use binomial formula. 


32. Monomial Formula for Velocity. 

It is necessary, from what precedes, to have a formula for 
velocity that can be used when the binomial formula ceases 
to apply. 

It is deduced as follows : The values of the modulus for 
all powders in use vary between narrow limits (0.6 to 1.0). 

Hence, assuming the equation (109a), 

A*) = 4**[3 - *\ 
we may place 

f{x) = Nx», (116) 

since when a variable changes its value within narrow 
limits, the function is proportional to some power of the 
variable properly chosen. It is necessary now to find the 
proper value of n in (116). / 

Differentiating (116), we have 

Substituting for f'{x) and /(*) their values from (109a),, 
we have 

f(x) _ 3 1 - * 

« = x- 

f(x) ' 2 3 — X 

for the value of n required. 



Assume equation (i 10) ; and substitute in it for f(x) its 
value (116), and we have 

2 I fa\* cStdMw* „ „. 

v = 2 -a(3B)-w[Jl)— -jt- *"■ • • C»8) 

Substitute for x its value (107a), and make 

M =jA(3£)"~W, (119) 

and we have 

*=^y(ir ^Tf +2 ~ - ■ • • (i2o) - 

pi 2 

Formula (120) is a general form of the binomial formula. 
(1O4), and will give the same values for v as the binomial 
formula, if the proper values for n be substituted. For the, 
particular case when x = T 9 T and n — \ (120) becomes 

v = m (t) (x) —p*- ^ I2I > 

This equation (121) is strictly applicable only to the par-, 
ticular case for which it was deduced ; that is, for x = T 9 T 
and n — i ; but by examining it we see that v increases con- 
tinuously as r decreases, which should be the case, while in 
the binomial formula, as already shown, v ceases to increase 
as r decreases. 

Hence if we use equation (121) for all values of x equal 
to or greater than £-, we will obtain a value for v which is. 
correct for the value x = ^-, and for all values of x greater 
than T 9 T , values for v which will be more nearly correct than 
those given by the binomial formula. 

This is called the " monomial formula" for velocity, and 
we say that it is used whenever the subtractive term in the 


binomial formula is greater than 0.273 ; since when that is 
the case the binomial formula is no longer applicable. 

When the subtractive term is nearly equal to 0.273, either 
formula can be used. 

, The monomial formula is usually written 

v = M afi-&2** (I22) 

by substituting a and /? for their values, equation (92). 

To find M, Sarrau assumes a type powder as before, 
making / = 1, r= 1, and thus determines ex and /?. The 
powder is then fired in a given gun, v measured, and thus 
everything is known in (122) except M, which may be cal- 

Its value thus determined is 

log M= 2.84571. 

33. Calculation of the Value of r. 

For the type powder r = 1, and under this supposition 
the values of A and B are deduced. The values of r for all 
other powders must therefore be expressed in terms of the 
type powder as unity. That is, the value of r for any pow- 
der is the ratio of its true time of burning to that of the 
time of burning of the type powder. 

The force of all nitrate powders is practically constant, 
as has been shown ; and since /= 1 for the type powders, it 
may be assumed as unity for all powders as an approximate 
value. Making /= 1 in the binomial formula (104), we have 

— ©'<-<)•[. -^]. • • <-> 

For any particular powder to which this formula is ap^ 
plicable, we could measure v and determine t, since all the 
other quantified are known, if the equation could be solved 
for r. But it is found that this solution is impossible. 


If the monomial formula applies to this particular pow- 
der, we have, making /= i, 

In (125), placing 

X = v pU < I26 > 

we have 


v — 

* = -Ti - ' ( I2 7) 

and this may be easily solved and the value of r obtained. 
For any powder, however, we do not know beforehand 
whether the binomial or the monomial formula is applicable, 
since t must be known to determine this point. Again, 
while the value of /is very nearly unity for all powders, it 
is not exactly unity for any except the type powder, and 
hence the value of t determined as above by the monomial 
formula would not be correct. ' 

Under these circumstances we proceed as follows : The 
value of t determined by (127) is approximate, but the 
approximation is sufficiently correct to show which formula 
is to be used. Substitute the value of r from (127) in the 
subtractive term of the binomial formula 

y = B r l T O28) 

If the result obtained is greater than 0.273, the monomial 
formula applies ; if less than 0.273, the binomial. 

Then calculate a by the pressure formula (103). Substi- 
tute this value of a in either the monomial or the binomial 
formula according as the former or the latter applies, as de- 
termined by the test, and solve for /3. This value of yS sub- 
stituted in the formula 

, = i 


will give r. The value of r thus obtained, substituted in the 

« = (#'■ 

together with the correct values of a and a, will give/. 

34. Determination of the Characteristics a and (3. 
1st Method.— We have, equation (92), 

Assuming /= 1 for all powders, we can calculate a and A. 
for any service form ol grain by the methods already ex- 
plained, and illustrated in the case of the spherical grain ; 
r can be calculated by the method explained above, in terms 
of the type powder as unity, and hence we find a and /3. 

2d Method. — In the second method we find the values of 
a and yS directly, without determining /, a, A, and r, as 

The characteristics a and ft enter the binomial and mono- 
mial formulas (91) and (122), and a enters the pressure for- 
mula (103). Hence, for a given piece, powder, and projec- 
tile, if we measure accurately the pressure, and substitute it 
in (103), we can find- a, and substituting the measured veloc- 
ity and the value of a, just found, in either the monomial or 
the binomial formula, whichever is applicable, we can find (i. 

^d Method. — In the third method two different guns are 
used, and the velocities accurately measured under two dif- 
ferent conditions of firing. The results being substituted in 
the binomial formula, or in the monomial and binomial for- 
mulas together, will give two equations, containing the two 
unknown quantities a and /?, from which they may be ob- 

The following table gives data with reference to Ameri- 
can guns and powders, and was calculated from data fur- 
nished from the Ordnance Proving Ground, Sandy Hook, 





oo *-* en r- oo co co o :*n *n 

^j- oo CT 1 O* O 

to r^ oo oo 

i-i O oo vO 

m in r-. m co 

tJ- a* w en « 

o> o> 
en ^> 
vO u-i 

O cm Q Q cm Cm <m cm <m cm <i- 











































































o> en *-■ co en co oo 

c» en m m o m 

t en en o wo 

en en en en ^- w 

o "t 
r- i— m 

en o o 

o> t* i*- "^ ^o 

oo CO CO 

o o o o o- o 

O CM CM Cm Cm Cm -Q Q 

■fl- in O en O Cf 
m in Tf co « r- 

r*- oo M o> tJ- o 

O r-» co 

w <t oo m 
tn en in 

en en vO 

\0 M vO 

en O O 

in vo r* 

O O 0> m 
a» vo en 

-* co « in 

vO O 
en CM 

in r}- ff^ O 

O* en ^" O 

CT» m vO in 

<*• O **■ ■* vO 

cm « en en 

























C* 0"* vO co oo Ovr^inco 

tno*vo en-rj-vo w m o oo oo 

co co r» en r- r*. en vo r*. « in o 

ococo r*- co co oo co o* Ov O O O 

in in co O 

O O O O O 
in in w vO co 

W -^" in O 






















































































N vO r- oo 

O en in in w 


O M 

O vO 
O en 
O* vO 

VO C4 C4 N o 
O C» 0> Ov I s " 

vO M 0> N vO 
en r- vo i— m 


en en rj- 

in in in 

en co co 

N « vO VO 

ci « vO n «. 

s s s 

CO Cr , 0>0 > 00>OCOcOOO oo* 

m u u u 

- !S S S 

Vi 5 5 2 

.« J J J 

.« M 03 CQ 

o , 

a s s 

, (A X 


»; -i iJ 


V 4) 

O C "1 ■- 

33 ° 

^ n «\ooCQ0QP3P3 

« 5 a (K S S 

J _j J J J J 

ca dq 03 m m m 

"o "« "m to "n *« 




35. Effect of Variation of Elements of Loading upon Velocity, and 
Maximum Pressure. 
The variable elements of loading for any gun are : 

1. The weight of the charge of powder, <S 

2. The density of loading, A. 

3. The time of combustion of the grain, t. 

The fixed elements are : 

1. The calibre, c. 

2. The travel of the projectile in the bore, u. 

3. The weight of the projectile,/. 

For the same force of the powder and the same form of 
grain, having c, u, and p constant, we may vary w, A, and r 
so as to obtain the same muzzle velocity with a different 
maximum pressure on the breech, or the same maximum 
pressure with a different muzzle velocity. In this discussion 
the maximum pressure on the breech is alone considered, 
since it is always greater than that on the base of the pro- 
jectile. There are an infinite number of sets of values of 
«3, A, and r which will satisfy these conditions, and the ques- 
tion is to determine what set to use. 

Assume equations (no) and (112), and regarding w, A, 
and t as variables, take the Napierian logarithms of both 
members of each, differentiate, and we have 

dv \doo , \dA fix) , , x 

— = §-— H T + -iH;dx\ .... (129} 

v 8 00 ' 4 A f(x) v y - 

dP a _idw dA dx 

-p;-^-£ + ~A + ^ (I3 °> 



* = *. 


T,dT r x dt dt 

dx = --jr=-- — =-X T . . . . (131) 


We have also, from (i i6#), y 


Substituting these values in (129) and (130), we have 

dv \ da> , 1 dA dr 

V = 8^+4^-*7 ; < I32 > 

dP. \dw , dA dr 

T^^T + T-T ( r 33> 

These equations show that when w and A increase, v and 
P, increase, and when r increases, v and P decrease; and 
this should evidently be the case. 

36. Change of Velocity when Maximum Pressure remains Con- 
stant — Fixed Powder-chamber. 

Variation of Velocity.— A gun, like any other struc- 
ture, is built to stand a certain fixed maximum pressure, and 
this pressure must not be exceeded. Therefore the most 
important consideration is to find how the velocity will 
vary for such changes in c5, A, and r as will keep the maxi- 
mum pressure constant and within limits. 

To do this we will consider the three variables w, A, and 
t in order, keeping one constant and varying the other two, 
and find the effect upon the velocity, the pressure being 
always constant and a maximum. 

1st. & constant, A and r variable. — Since P t and <£> are 
constant, we have 

dP, = o ; dw = o ; 

and hence, from (133), 

dA dr 

A ~ x 



This condition must hold in order that P t be constant. 

Substituting the above value of — in (132), we have 

dv dA 

- = (£-«)— (134) 

The value of n is, from (117), 

3 1 — x 

n-- . 

2 3 — x 

When the modulus x > 0.6, which corresponds to a very 

slow powder, n < \, and hence — is positive and increases 

with A. Therefore, when the weight of the charge is con- 
stant, we see from (134) that we may increase the velocity 
by increasing the density of loading ; but in order to keep 
the pressure constant, (133^) shows that we must use a slower 

2d. A constant, g5 and r variable. — P„ and A being constant, 

we have 

dP = o; 

dA =0; 
and from (133), 


3 dw dt 

4 00 r 

for the condition that P shall be constant. 

Substituting this value of — in (132), we have 

dv 3/1 \d<3 

— = - *— (135) 

v 4V2 / 00 JJ ' 

The value of n is 

«= (i35«) 

2 3 - x \ JJ / 


When x = o, n = %. It is less than i for every other 
value of x. Hence ($ — n) is always positive, and — in- 
creases with c3. • 

Therefore when the density of loading is constant, (135) 
shows that we may increase the velocity by increasing the 
weight of charge, but {134a) shows that in order to keep the 
pressure constant we must also use a slower powder. 

This means that we can obtain an increase of yelocity 
with a constant maximum pressure, by increasing the size 
of the chamber and using a larger charge of slower 
powder, and this is the general method employed at present. 

3d. r Constant, & and A Variable. — P a and r being con- 
stant, we have 

dP =o; 
dr = o ; 

and from (133), 

3 dw dA 

4^"=- -4 tas*) 

for the condition that P„ shall be constant. 

Substituting this value of -j- in (132), we have 

dv 3 dw 

V == 76~£ (*3 6 ) 

Since this is always positive, (136) shows that for the same 
kind of powder we may increase the velocity by increasing 
the weight of charge, but (135-S) shows that in order to keep 
the pressure constant we must also decrease the density of 

Fixed Powder-chamber.— In the preceding discussion 
it has been supposed that we could vary the size of the 
powder-chamber. But in the ordinary case, with a gun 
already built, the powder-chamber will be fixed and its 
volume constant. In this case we have 


Taking the Napierian logarithms of both members and 
differentiating, we have 

dA doo , 

-A=-& ( J 37) 

Substituting this value of -j in (132) and (133), we have 



The variables are thus reduced to two. Now if we sup- 
pose 00 and x to vary so as to keep P, constant, we have 
dP, — o, and from (139) 

dr _ 7 dcd 

r ~ 4 00 ' 














for the condition that P shall be constant. 

Substituting this value of — in (138), 

dv 7 / 5 \dw 

— = -I— n\^r (141) 

V 4\li I 00 \ t ) 

When x = 0.6, n = \ (see 1350) ; and for larger values of 
x, n becomes smaller ; therefore for all cases in practice the 
second member of (141) is positive, and v increases with w. 

Hence (141) shows that when the powder-chamber is 
fixed, we may increase the velocity by increasing the weight 
of the charge, but (140) shows that in order to keep the 
pressure constant we must use a slower powder. That is, 
we use a larger charge of slower powder. 

37. Relative Variation of Velocity and Time of Combustion — Of 
Velocity and Maximum Pressure — Limits of Modulus — Use- 
ful Practical Formulas. 
Velocity and Time of Combustion. — To determine 

the relative change in velocity for a given change in the 


time of combustion, suppose r to be the only variable in 
equation (132). Then 

dab = O ; dA = o ; 

and the equation becomes 

dv dr . 

— =— « — (142) 

As powder becoms slower x decreases. But as x de- 
creases n increases (see 135a). In fact, n may be called the 
"modulus of slowness," since it increases as the powder 
becomes more slow, while x, or the " modulus of quickness," 
increases as the powder becomes quicker. From (142) it is 
evident that for the same relative change in the time of 
burning the effect upon the velocity will be greater as the 
powder becomes more slow, since n becomes greater. 

This is one of the principal objections to using very 
slow powder, because small irregularities of manufacture, 
which are always apt to occur, affect r, the time of burning, 
and cause irregularities in velocity. 

Velocity and Maximum Pressure. — In the same way, 
to determine the relative change of velocity and maximum 
pressure, suppose t the only variable in equation (133). 


dw = o ; dA = o ; 
and the equation becomes 

dP t dr 

P' r 

Substitute this value of in (142) and we have 



dv _ dP a 

v n p: 


From this we see, generally, that with quick powders, 
since n is small, a given increase of pressure gives only a 


very small increase of velocity, and for slow powders, since 
n is large, a given increase of pressure gives a considerable 
increase of velocity. Hence it is advantageous on this 
account to use slow powders. 

Limits of the Modulus. — The preceding considera- 
tions may be applied in fixing the inferior limit of the 
modulus as follows : 

Equation (144) shows that as x decreases, or n increases,. 
a given increase in the pressure will give a considerable 
increase in the velocity, and hence it appears to be advan- 
tageous to use a slow powder, for which n is large. But 
(142) shows that for large values of n we have great irregu- 
larities in v, as previously explained, and Sarrau has fixed 
upon 0.6 as the value of x below which it is not expedient 
to go in practice in order to avoid these irregularities. 

For the superior limit, when x = -fa- or n = \, equation 
(144) shows that the relative increase of velocity is only one 
eighth that of the maximum pressure ; and since the mono- 
mial formula was deduced for this value, it was formerly 
regarded as the superior limit of the modulus. Other con- 
siderations, however, have led to an increase of this value 
up to 1.2 for some powders. 

Useful Practical Formulas. — In practice it is fre- 
quently required to find what change in velocity and press- 
ure a given change in weight of charge will produce in the 
Same gun. For this purpose assume the monomial formula 
for velocity 

v — Ma3-t — . 


For any other charge of the same powder whose weight 
is do", all the quantities in the formula will remain constant 
except v, do, and A. The value of A is 

27.68c3 „ „ 

c = Kw> 


K being a constant. Raising both members to the one- 
fourth power and multiplying by &, 

GOiAi = Kiwi. 

Dividing the value of v by that of v', we have 

v> = &i <*45) 

Similarly, for the pressures we have 

Ado* = Ka$. 
Dividing as before, we have 

P. _ <», 

PI cd'i 


These formulas are correct for quick powders and ap- 
proximately correct for slow ones. The velocity formula 
is useful where it is necessary to find the charge required 
to give a certain velocity to a projectile at a target at re- 
duced range, as in armor-plate experiments. 

38. Pressure Curves in Guns— Noble and Abel's Method — Mayev- 
ski's Method. 

It is necessary in designing a gun to know the pressures 
at different points along the bore, as the projectile moves 
through it, under the action of the powder-gas, in order that 
the gun may be given sufficient strength to withstand these 

The accurate solution of this problem is attended with 
great difficulties, and can hardly yet be said to have been 
successfully accomplished. Enough is known, however, to 


furnish safe working limits in designing the strength of the 
gun at different points. 

Noble and Abel's Method.— They assumed an ex- 
pression of the form 

x = at" + v + v t ', (147) 

in which x is the distance travelled by the projectile, t the 

iti — \ — \ — 1 n , 

T ";.a&#ar - 


Fig. 9. 

corresponding time, and a, a, /?, and y constants to be deter- 
mined by experiment. 

Wires were inserted into a gun through holes drilled at 
short intervals, as shown in Fig. 9. These wires carried 
currents of electricity, which were broken by the projectile 
in its passage through the bore, and these breaks were re- 
corded on the Noble chronoscope, which is an instrument 
for measuring very small intervals of time. 

The distance between the holes gave x, and the record 
of the chronoscope t, and substituting the values thus ob- 
tained in (147), the most probable values of the constants 
were determined by the method of least squares. 

Differentiating (147) with respect to t gives 

A* / ON 

*= v > < I48 > 

and differentiating this with respect to t gives 

d'x _ dv 


the acceleration. 

If W be the weight of the projectile and P the total 
pressure on its base, we have 


Mayevski's Method. — General Mayevski assumed 

x = At + Bt 2 + Ct' + Dt' + etc (151) 

and by experiment determined /, having x given by the 
nature of the experiments (see Fig. 10). His general plan 
resembles that of Noble and Abel, but differs in the method 
of conducting the experiments. 

\\ fl 


n // 




block, b v •; ; 


Fig. 10. 

From these results values of A, B, C, and D were deter- 
mined by the method of least squares. 

Differentiating (151) with respect to t, we have 

v = 


A + 2Bt+ iCt % + 4Df + etc., 


for the velocity at any point. 
From (152) we have 

dv tPx „ . , - 

di z= d7 = 2B + 6Ct+12Dt '+' etc -> ■ ■ ■ 053) 

for the acceleration ; and for the point where this is a maxi- 
mum we have, from (153), 

^r = 6C+24Z?/ + etc. = o (154) 

39. Longridge's Method. 

Mr. Longridge, an English engineer, uses a combination 
of Noble and Abel's and of Sarrau's formulas as follows : 

Noble and Abel's formula for the pressure curve is see 

/ .432;' v° 74 




in which / is the pressure corresponding to the volume 
v", v' is the volume of the powder-chamber supposed to be 
entirely filled with powder, and v" any other volume of ex- 

Fig. ii. 

Let AB, Fig. n, represent the reduced length of the 
powder-chamber, that is, the length of a cylinder whose 
diameter is that of the bore and whose volume is that of 
the powder-chamber. 

Suppose, according to Noble and Abel's hypothesis, that 
all the powder is burned before the projectile moves from 
its position B. Make v" = v' in (155), and we have/ = 43 

This is the pressure that would exist in the chamber if 
the powder were all burned before the projectile moved. 

Lay off BB' = 43 tons. Assume different values for v" , 
corresponding to C, D, E, etc. Calculate the corresponding 
ordinates from (155), and erect them at the corresponding 

The resulting curve B'C'D'E will be Noble and Abel's 
pressure curve. 

Now it is known that the powder is not all burned before 


the projectile moves, and hence the pressure BB' — 43 tons 
cannot exist in a gun. 

The maximum pressure that does exist is given by Sar- 
rau's formula for the maximum pressure on the breech. 

P = K a i Ap'& i c-\ 

Calculate this pressure, lay off AA' at the breech equal 
to it, and assume this pressure to be uniform from the breech 
to the point of maximum pressure in the bore. Substitute 
this value of P, for p in (155) and find the corresponding 
value of v". This value of v" will give the point P in the 
bore at which the maximum pressure occurs. The line A'P' 
will be parallel to AP, and the curve of pressures will be 
A'P' CUE. 

Let #, — AB, the reduced length of the powder-chamber; 
x = any other length measured from A. Then 

v' = nr'x^ ; 
v" = nr'x; 

and equation (155) becomes 

/ = 43-U _ -5; \ , (156) 

which is more convenient for use. 

The pressure at B is originally zero and rises to a maxi- 
mum at P' . Hence the actual pressure curve has the form 

The form of the curve from B to P' is not important, as 
its maximum ordinate only is required. 

40. Pressure Curve by Sarrau's Formulas. 

The pressure curve in a gun may also be obtained from 
Sarrau's velocity formulas, as follows: 

For a slow powder we ,have 

v = A«{*)*$[i-Bp&t\ . . (I5 64 


In (156a) u is expressed in inches. In (161), following, z» 
and g are in feet, and u must be expressed in feet in order 
that, when du is substituted in (161), all the quantities may- 
have the same unit. 

Hence in (156a) we write 

u % inches = 12V feet; 
and in the subtractive term 

«* inches = 12V feet. 

v — au\i — du*), ........... 057)i 

in which u is in feet, and 

Aao^A* X 12* 


From mechanics we have 

P = m dt> 

du = vdt; .'. dt = 



, = ^X 12 * (159) 

Substituting in the value of P', we have 

„, vdv p vdv , _ „ 

f* = m-r- = - -j- f (l6ctf* 


p being the weight of the projectile, and m its mass ; and if oo 
denote the area of the base of the projectile in square inches, 
we have for the pressure in tons per square inch on its base, 

i> vdv 

P" = — £ — -5- (161) 

224000^- du v ' 

Differentiating (157), we have 


dv 3 7 , , 

du 8 - 8 

vdv 3 „ c 7 


{ja'u-i - -a'tui -f |«V»tJ. (163) 

pn / 

2240 X 00 x £■ L8 4 

For quick powders we have 


v = ^ •; 

which may be placed in the form 

v = a'u?*, . . . . , 
u being in feet as before explained, and 
, _M<K/3-*clkl i c i X 1 2* 


Differentiating (164), we have 



dv 3 

d^ = T6 au ' H ' («*) 



vdv x , 

A=f6 a «" 1 < l6 7> 


/"'= — (-^a n ic-i\ . . . (168) 

2240 X <*>Xg 

Since these curves are obtained on the adiabatic hypothe- 
sis, they may be considered as marking the inferior limit of 
pressures, and the true pressure curve probably lies between 
the latter and those obtained by Longridge's method". 

It must be remembered that the pressures given by these 
equations {163) and (168) are those producing motion of the 
projectile, and do not represent the total pressure on the 

41. Determination of Velocity by Experiment — General Principles 
— Targets for Cannon — For Small Arms. 

In order to verify the formulas for velocity and pressure 
previously deduced, it is necessary to determine accurately 
by experiment the velocity of the projectile, and the pressure 
in the gun, due to a given charge of powder, under given 
conditions of loading. 

VELOCITY. — The velocity of a projectile is determined by 
measuring the time of its passage over a given distance. 

Let A and B be two points whose distance apart is s, and 
t the time of passage of the projectile over this distance. 
Then, since 

v = f 

v will be the mean velocity of the projectile over the dis- 
tance s, or its velocity at the middle point between A and B. 
In order that this may be true, the space s must be so small 
that the motion of the projectile may be considered uniform 
and in a right line. As neither of these conditions holds in 
practice, v will not be the velocity at the middle point be- 
tween A and B, but it will be sufficiently correct for all 
practical purposes to assume that it is. 


General Principles.— In order that we may know ex- 
actly the time of passage of the projectile over the distance 
s, we must have first an accurate scale of time, and second, 
we must mark on this scale the instant that the projectile 
passes the two points A and B. The difference between the 
times of passage of the points A and B will then give the 
time of passage over the distance s, and knowing this time 
we can find the mean velocity. The passage of the projec- 
tile over the points A and B is marked on the time-scale as 
follows : 

Two targets are set up, one at A and the other at B. 
Electric currents circulate through these targets, and 
also through the instrument which furnishes the scale of 

When the projectile passes the target at A it breaks the 
circuit, and this break is registered by the instrument. 
When it passes B the same thing occurs. The differ- 
ence between these breaks measured on the scale of 
time, and corrected for errors, gives the time of passage 

Targets for Cannon. — The functions of the targets are 
then to mark the points in the path of the projectile between 
which its velocity is to be measured, and to support the 
wires carrying the electric currents which are to be broken 
by the passage of the projectile. For cannon, the first target 
is placed at such a distance from the muzzle that it will not 
be injured by the blast. Call this distance x x , and the dis- 
tance from the muzzle to the middle point between the tar- 
gets x ; then 

■ s 

X = X. + . 

1 ' 2 

The velocity found by experiment is at the point — , that 

which we wish to find is at the muzzle, or the initial velocity. 
By formulas in " Exterior Ballistics " we can find the latter, 
when the former, at the distance x, is known. 

Each target for cannon generally consists of a frame of 
wood carrying a number of small parallel copper wires. 





The wires are so arranged that the current entering one 
side of the target must traverse all of them before 
passing out at the other side, so that the breaking 
-of any wire will break the current. The wires are 
drawn as tight as possible in order that the break 
may be abrupt, and the distance between them 
depends on the diameter of the projectile, as it 
must be impossible for it to pass through with- 
out breaking at least one wire. The breaks are 
repaired after each fire. 

The target is shown in Fig. 12. 

Small-arm Targets. — As there is practically no blast 

with small arms, the first target is placed at the muzzle, and 

-consists of a single wire drawn tightly across it. To avoid 

repairing the second target, it consists of a steel plate to stop 

the bullets. On its rear face is 
secured a spring insulated from 
the plate (Fig. 13). This spring, 
s, is fixed at one end to an insu- 
lating substance, such as a block 
of wood, w, and the other end 
The current passes through the 
spring and pin. When the bullet strikes the steel plate, the 
shock causes the spring to leave the pin, and thus the current 
is broken. The elasticity of the spring causes it instantly to 
resume its former contact with the pin, and thus renders any 
repairs unnecessary. 

Fig. 13. 
rests on a metallic pin, p. 

42. The Ballistic Instruments — Description of the Le Boulenge 

The functions of the ballistic instruments are to furnish 
an accurate scale of time, and to record on that scale the 
rupture of the targets by the passage of the projectile. 

Le Boulenge Chronograph. — The instrument gener- 
ally used for this purpose was invented by Captain Le 
Boulenge' of the Belgian Artillery, and is called the Le Bou- 
lenge' Chronograph. 

Scale of Time — Its scale of time is furnished as follows : 

Two rods are suspended vertically from electro-mag- 



nets, and the currents which pass through the magnets 
pass also through the targets. Each electro-magnet has its. 
own current and its own target, and is independent of the 

When the first target is broken, one of the magnets is 
demagnetized and its rod falls. When the second target is 
broken, its magnet is demagnetized and its rod falls. The fall 
of this second rod makes a mark on the first rod while it is 
falling, and the distance h' from the origin of fall to this 
mark is measured. Then we have, from the laws of falling- 

h' = igT* 

= V7' 


which furnishes the scale of time. 

Record of Breaking of Target' 
— Description of Instrument. — 
The method of making the 
record will appear from a de 
scription of the instrument, Fig. 

Its principal parts are a ver- 
tical column of brass, B, which 
is supported by a triangular 
bed-plate, C, and this bed-plate 
rests upon a support or stand, 
5. To the brass column are 
attached two electro -magnets,. 
EE'. The magnet E supports, 
the long rod a of the instru- 
ment, called the chronometer. 
This rod when in use is en- 
veloped by a zinc or copper 
tube, z, called the recorder, 
upon which the mark is made. 
The magnet E' supports the 
short rod b, called the regis- 
I'ig. 14- trar. 

Fig. 15 shows the details of the marker, or part of the- 













instrument which makes the record of the breaking of the 
target. It consists of a cir- 
cular knife, m, on the end of 
a spring, s, which causes it 
to move to the right in the 
figure. The trigger, /, is 
supported in its fulcrum on 
the bed-plate. Its right end 
terminates in a catch, which 
engages in a corresponding 
one on the knife, and pre- 
vents the latter from moving 
to the right, under the action 
of the spring, till the catch is 
freed. The left end of the 
lever is acted on by a spring 
/, which presses it upwards, 
and keeps the catch engaged 
with the knife. The piece marked b is a disk which screws 
into the left-hand end of the lever, and which may be raised 
or lowered by means of the screw. 

Above the disk is a tube or cup which retains the short 
rod b after its fall. The record is made by the short rod 
falling on the disk b, depressing it, and releasing the knife 
m from the catch on the trigger. The knife then moves to 
the right and, striking the long rod in its fall, makes the 
required record. 

43. Arrangement of Wires — Working of Instrument — Disjunction. 

Arrangement of Wires. — The arrangement of the 
wires depends upon whether the time to be measured is 
comparatively great or small. When great, the wires are 
arranged as follows, Fig. 16. 

The chronometer is supported by the upper magnet. The 
first current comes from the battery to the upper magnet, 
E\ from the magnet E to the disjunctor, whose functions 
will be explained later ; from the disjunctor to the first target, 
and from the first target to the battery. The course of the 
second current is similar and can be readily followed. 



The instrument thus arranged k called a megagraph. 
Working. — When the first target is broken, the chronom- 
eter falls ; when the second target is broken, the registrar 

Fig. 16. 

falls, and, striking the disk of the trigger, makes the record 
on the chronometer, as at R, Fig. 14. 

The point on the chronometer from which all heights 
are measured is the mark O, Fig. 14, made on this rod by 
the knife when the chronometer is suspended by its magnet. 
Denoting the height OR by h', the corresponding time is 


and is the time which elapses from the fall of the chronom- 
eter till the record is made. It is not, however, the time of 
passage of the projectile between the targets, because — 

1. There is a certain time required for the demagnetiza- 
tion of the magnet E. Hence the chronometer does not fall 
at the instant the first target is broken, and the time is too 
short by this amount, which we call t x . 

Instead of making the record the instant the second 
target is broken, there is a delay caused by — 

2. The time required to demagnetize E' = I,. 


3. The time required for the registrar to fall to the disk 
of the trigger = t,. 

4. The time necessary to disengage the trigger, and for 
the knife to move forward and make the record on the chro- 
nometer = t t . 

During these last three intervals the long rod is falling, 
and hence the height of fall, and consequently the time, is 
too great by their sum. Hence the true time is 

t = T-{t,+ t t + t t ) + t„ 

and to find the true value of t it is necessary to find the 
values of these times, since T is known. 

To do this it is not necessary to find the value of each 
single interval, since the total time can be readily obtained. 
If we break both currents at the same instant, it is evident 
that all the delays mentioned will still exist. The delay in 
falling of the chronometer, and that of making the record 
by the registrar, will be marked on the long rod as it falls, 
and will be found at a certain height above O, as at D, Fig. 14. 
This height is called " the disjunction," and the time corre- 
sponding to this height is the algebraic sum of all the times 
before named. 


* = (', + '. + '.)-'.• 

V S ' 
in which h is the height OD. Hence 


It must be remembered that difference of times and not 
difference of heights is to be taken. 

Fixed Disjunction. — For the velocity at the middle 
point between targets we have 




Substituting for / its value, we have 


v = 

Izh' Izh 

From this equation we see that if the values of s, and of 

— or the disjunction, be fixed, the values of v can be 

calculated and tabulated for all values of h' within the 

limits of practice. This has been done for the values 

V ; 



ioo feet and a/ — = 0.15 second, and this value of 


— is called the fixed disjunction. If the above table is 

not at hand, this fixed value of the disjunction avoids the 

labor of calculating: 6 or a / — for each shot. 

V g 

Hence in this case 

/ = T — 0.15 sec. = a / 0.15. 

V g 

To fix the disjunction, the disk b on the trigger / may- 
be raised or lowered to regulate the height of fall of the . 
registrar till = o. 1 5 sec. 

44. Arrangement of Wires for Small Times— Disjnnctor— Measur- 

Arrangement of Wires.— Under ordinary conditions, 
the distance between targets is so great, that the chronometer 
acquires considerable velocity in falling, before the record 
is made by the registrar. As the distance between targets 
decreases there will be less interval between the breaking 
of the two currents, and consequently between the fall of the 
two rods. Hence the record will be made before the chro- 
nometer has acquired much velocity, and small differences 




in reading will correspond to considerable differences in 
time. A small error in reading, therefore, will correspond 
Jo a large error in time. As the distance between targets 
decreases, the record will approach the disjunction circle, 
and will fall on that circle when the distance is zero, or 
when both currents are broken simultaneously. To measure 
these short intervals of time accurately it is necessary to 
allow the chronometer to acquire considerable velocity 
before the record is made upon it. 

This necessitates a new arrangement of wires and mag- 
nets, as in Fig. 17. The magnet which supports the regis- 
trar is changed from below to 
above that which supports the 
chronometer, and the first cur- 
rent runs from the battery to 
the registrar magnet, thence 
to the disjunctor and to the 
first target, so that the regis- 
trar will fall first. With this 
arrangement, if both currents 
be broken simultaneously, the 
"disjunction" will be made 
near the top of the chronom- 
eter at D, when its velocity is 
greatest. When the registrar 
falls first, as it does in actual 
use in determining velocity, it 
is evident that the record will 
be made at some point be- 
low the disjunction, as at R. 
The same method is followed 
in determining the time as be- 
fore, except that the time cor- 
responding to the record must" 
be subtracted from that corre- 
sponding to the disjunction, for the time of passage between 
targets. The instrument thus arranged is called a micro- 

Disjunctor. — This instrument is used for breaking both 



'■. ,Jlai 



Fig. 17. 

9 2 


currents simultaneously in order to determine the alge- 
braic sum of all the times *,, t„ t 3 , etc. 

It consists (Fig. 18) of two steel blades, »«', mounted on 

Fig. i 8. 

a block of wood. These blades are attached at one end,. 
m ni ', to the block, and carry binding-screws at this end. At 
the other end they rest on two brass pins, b b', and these 
pins are connected with the binding-screws shown. Be- 
tween these blades is a strong spring, r, with a knob, s, and a 
spring-catch, g. At right angles to, and attached to this 
spring r is a cross-piece, pq. The action is as follows : 

When the spring r is pressed down by pushing on the 
knob s, it is caught and held under the spring-catch g i and 
the cross-piece is not in contact with the blades n n'. 

Under these circumstances the blades rest on their pins 
b b', and the current from each battery enters its own blade 
by the binding-screws and posts, and passes to its target. 

But when the trigger or catch g is pulled back quickly, 
the spring r is released, and, rising, its cross-piece pq strikes 
both blades n n' at the same instant, lifts them from the pins 
b b', and breaks both circuits. 

Measuring-rule. — To facilitate measurements, the 
heights corresponding to all velocities within the ordinary 
limits of experiment are inscribed on a metal rule furnished 
with a sliding index. The heights are in millimetres, and 
must be reduced to feet for use with English measures. A 
table of times corresponding to heights in millimetres has 
been calculated, and by its use the above reduction may be 
avoided. The sliding index has a knife-edge attached to it, 
and, to obtain the reading, this knife-edge is placed on the 
mark made by the marker on the chronometer, a pin on the 
lower part of the scale having been inserted in a hole in the 


chronometer at the lower end to bring the zero point of the 
scale opposite the origin of fall. The height can then be 
read off. 

45. Adjustments — Use — Objections to the Instrument — Br6ger's Im- 

Adjustments. — The instrument must be properly 
mounted on a stand at such a distance from the gun that it 
will not be affected by the shock of discharge, and connected 
with the batteries and targets, and be then adjusted for use. 

The adjustments are three : 

1. Levelling. — The object of this adjustment is to make 
the bed of the instrument level, and consequently the brass 
column or standard vertical. The chronometer is used for 
this purpose. The enveloping tube or recorder is first put 
on, and when in place must rest closely against the bob. 
Having cocked the knife, suspend the chronometer and 
recorder from its magnet, and move the levelling-screws 
which pass through the bed-plate, till the bob of the chro- 
nometer rests in a square notch in the bed-plate. The stand- 
ard is now vertical, 

2. Regulating the Magnets. — To regulate the strength of 
the magnets, each of the rods is provided with a weight 
which is one tenth that of its rod. Place the proper weight 
on the chronometer, and suspend it with this weight from its 
magnet, the core of which is movable, and draw out this 
core till the rod and weight fall. The strength of the 
magnet is by this means regulated. Do the same for the 
short rod, or registrar, and its magnet. 

3. Fixing the Disjunction Reading. — For the megagraph 
this reading is at a fixed height, corresponding to 0.15 
second. To make the adjustment, place the sliding index 
on the rule at the mark " disjunction," and clamp it. 

Place the pin of the rule in the hole in the bob of the 
chronometer, bring the knife-edge of the rule to bear against 
the copper tube on the chronometer, and turn this tube 
around the chronometer. The knife-edge will describe a 
circle on this tube, called the " disjunction circle," and the 
disjunction reading must fall on this circle. To test it, 


suspend both rods from their magnets, and break both cur- 
rents by means of the disjunctor. If the mark made by the 
knife falls on the circle, no adjustment is necessary ; if 
above the circle, the fall of the registrar is too great ; and 
if below, the fall is too small. The height of fall of the 
registrar is diminished or increased by raising or lowering 
the disk on the left-hand end of the trigger t. The instru- 
ment is now ready for use. 

Use. — In using it, first cock the knife or marker, suspend 
the long and short rods, and take a disjunction reading. If 
the disjunction is not exact, correct as above. If exact, 
cock the knife again, suspend the rods, fire the piece, and 
read the height with the rule. Find the time corresponding 
to this reading, subtract from it the time corresponding to 
the disjunction, which is 0.1.5 second whenthe instrument 
is used as a megagraph ; or if used as a micrograph, sub- 
tract the time corresponding to this height from that corre- 
sponding to the disjunction, as previously determined, and 
the remainder will give the time of passage of the projectile 
between targets. Divide the distance between the targets 
in feet by this time in seconds, and the quotient will be the 
velocity of the projectile at a point midway between the 

Objections to the Instrument. — The principal source 
of error in the Le Boulenge arises from the fact that the 
circuits are not broken similarly by the disjunctor and by 
the projectile. 

When the circuits are broken by the projectile, the re- 
tardation of demagnetization is modified, and unequally so 
for the two magnets, because they sustain different weights- 
and are consequently of different strength. 

Bregek's Improvements.— This has led to modifications 
of the instrument by Captain Br<§ger (Fig. 19). The princi- 
pal of these are, the two rods are made of exactly the same 
weight, and consequently the electromagnets are of the 
same strength. Their axes are vertical instead of horizon- 
tal. The parts generally are heavier and more firmly sup- 

The height of fall of the registrar is regulated by raising 



or lowering its magnet, £', and the disk of the trigger on 
which the registrar strikes is fixed 
with reference to the lever. The 
knife is square instead of circular. 
The disjunctor has been modified 
so as to insure the simultaneous 
rupture of the two circuits, and 
the strength of the currents is reg- 
ulated by resistance-coils. These 
improvements render the instru- 
ment much more accurate than 
the old form. 


Fig. 19. 

46. Schultz Chronoscope — Marcel- 
Deprez Registers — Bashforth Tar- 

Schultz Chronoscope. — The 
Le Boulenge Chronograph meas- 
ures velocity at one point only. 
If the velocity of a projectile is to 
be measured at several points, a 
separate instrument is required for 
each point, and this arrangement 
would be troublesome, besides hav- 
ing other objections. 

It is frequently necessary to 
measure the velocity of the same projectile at different 
points, as in determining the laws of the resistance of the 
air to its motion, and also it is sometimes required to deter- 
mine its velocity at different points in the bore. For such 
purposes an instrument must be used which will give a 
scale of time of such an extent that all the phenomena may 
be registered upon it. 

There are several instruments of this class, and as a type 
of them the Schultz chronoscope, one of the best known, 
will be briefly described (Fig. 20). 

Scale of Time. — In this instrument a cylinder a revolves 
by means of clockwork, and this cylinder has also, in the 
older form of machines, a motion of translation parallel to 

9 6 


its axis. In the most recent form the cylinder rotates only, 
while the point b, which describes the scale, has the motion 
of translation. 

The point b is a quill attached to one branch of a tuning- 
fork, c. This point may be made to rest lightly against the 
surface of the cylinder, or may be withdrawn from contact 
with it. On each side of the tuning-fork is an electro- 
magnet, d. 

The object of the magnets is to start the fork vibrating, 
to keep up this vibration during the experiment, and to 

Fig. 20. 

equalize the amplitude. The surface of the cylinder is-, 
covered with lampblack before using. When the quill is. 
placed in contact with the coated cylinder, the latter is set 
to rotating and the fork to vibrating. The quill-point will 
then trace on the cylinder a sinusoidal curve, and, the 
number of vibrations of the fork per second being known, 
we have an accurate scale of time. If the time to be 
measured is greater than can be registered on one revolu- 
tion of the cylinder, the cylinder or fork is given a motion, 
of translation along the axis, and the sinusoidal curve then 
becomes a helix, and the whole length of the cylinder can 
be used. 

Marcel Deprez Registers.— The record is made as foU 
lows: Small electro-magnets, ee, Fig. 21, are placed in front 



of the cylinder, above the time-register, 
with very light armatures, /, acted 
on by a spring, g, which is almost in 
equilibrio with the magnetic attrac- 
tion. A point, h, connected with the 
armature, rests against the surface of 
the cylinder. When the current at 
a target is broken, the correspond- 
ing armature f yields to the action 
of the spring g and is drawn aside 
quickly, the point h recording the 
motion on the cylinder by the side 
of the time-scale. The number of 
vibrations of the fork between any 
two breaks divided by the number 
per second gives the corresponding time, 
counting vibrations, the quill b, Fig. 20, is 
to trace a 

They are provided 

Fig. 21. 

To assist in 

first allowed 

simple helix before the fork is put in vibra- 

The quill-point is then returned to its starting-point. 

This line is called the mean helix. If the targets are at 
such a distance apart that the current which is broken at 
one point may be restored before the projectile reaches the 

next, one register and one circuit 
will be sufficient. If the targets 
are too close together for this res- 
toration of current, each target 
must have its own current and 
register. The registers have a 
motion of translation in common 
with that of the tuning T fork. 

Bashforth Targets. — For 
restoring the current as above 
described, the simplest device is 
theBashforth target, invented and 
used by the Rev. Francis Bash- 
forth in his celebrated experi- 
ments on the resistance of the air 
to the motion of projectiles. 

This target (Fig. 22) consists of a series of wire springs, bd,. 

Fig. 22. 


inserted in a board. On the front of this board are brass 
plates, ace, having oblong holes in them through which the 
springs pass. 

The springs are held down in contact with the lower 
side of the holes by weights, w w, attached to them by 
strings. The current entering the plate a, will pass through 
the wire spring b to the plate c, and so on. When one 
of the strings is cut by a projectile, the corresponding 
spring will fly up to the upper side of the hole in the brass 
plate c, and the current will be broken during the passage 
of the spring from bottom to top of hole, and will be made 
again as soon as the spring strikes the top. 

47. Determination of Pressures by Experiment — Static Method — 
Discussion — Conclusions. 
There are two methods of measuring a force or pressure : 
i. The Static Method, in which the unknown force is 

balanced by a known resistance ; 

2. The Dynamic Method, in which the unknown force is 

determined by the acceleration which it communicates to a 

given mass. Its measure is, from mechanics, 

dv d^s 

P= m - = m - 

Static Method. — General Principles. — The general 
method adopted in this case is to balance the unknown force 
by the resistance which a body offers to deformation. If we 
have a cylinder of metal of known length and diameter, and 
uniform in quality, and apply to it a known force in the 
direction of its length, the cylinder will be decreased in 
length by a certain amount. We measure accurately this 
decrease in length and note the force producing it. Pro- 
ceeding in this manner we can form a table one column of 
which will contain the decrease in length of the cylinder, 
and the other the corrresponding pressure for all pressures 
within the limits of experiment. From this table a curve 
may be constructed whose abscissas give the pressures, and 
the ordinates the corresponding compressions. 

Such a curve is called the " tarage" of the cylinder. 


If now a cylinder of the same material and dimensions be 
subjected to the force to be measured, and this force be 
•applied in the same manner as that producing the " tarage," 
it is only necessary to measure the compression produced 
by the unknown force, and find from the " tarage," or from 
the table, the corresponding pressure. 

DISCUSSION. — The pressure we wish to measure is that 
of the powder-gas. This gas acts upon the cylinder to be 
•compressed, through the medium of a piston whose area is 
exactly known. 

This piston moves in a cylindrical channel, and its head 
rests against the cylinder to be compressed, the gas acting 
upon the opposite end of the piston (see Noble crusher- 
gauge). In order that the results of the compression may 
agree with those of the " tarage," the mass of the piston and 
its velocity must be as small as possible. To show this: At 
any instant let 

P be the intensity of the force to be measured ; 
R, the resistance to deformation offered by the cylinder ; 
m, the mass of the piston ; 
v, its velocity ; 

x, the length of path passed over by it. 
The work of the pressure on the piston over the path x 



and that of the resistance over the same path 



and the difference between these is the energy of the piston ; 

imv' = f'Pdx - f X Rdx. 

I/O I/O 

In order that P= R, which is the condition sought, we 
must have at all times 

\mv — O. 


Now m cannot be zero, but it must be as small as possi 
ble, and v must also be small. The former condition is- 
attained by making the piston small, and the latter by com- 
pressing the cylinder before firing by a force nearly equaL 
to the value of P anticipated. 

Conclusions. — From numerous experiments Sarrau 
concludes : 

1. Gunpowder is the only explosive which under ordi- 
nary conditions produces compressions agreeing with the 
" tarage." 

2. This conclusion is true only when the gauge is in rear 
of the projectile. In the powder-chamber the pressure rises, 
from zero to a maximum in a short time, but the time is ap- 
preciable. Hence the application of the pressure resembles 
in some degree that of the force producing the tarage. 
When, however, the gauge is situated in front of the base of 
the projectile, the gas suddenly strikes it, upon the passage of 
the projectile, and we have a case similar to that of the high 
explosives, and the same rule applies as with them. (See 3.) 

3. For the high explosives, the rate of application of the 
force is so great that as a general rule the maximum press- 
ure is measured by the " tarage " corresponding to one half 
the compression of the cylinder. 

48. Rodman and Noble Gauges — Advantages of Noble. 

Rodman Gauge. — The Rodman Pressure-gauge, Fig. 
23, consists of a body or housing, H, which is a receptacle 
for all the working parts. A copper disk, C, is placed in 
the housing, and a knife, K, rests against it. The knife is 
attached to the piston P, which fits accurately in the cylin- 
drical hole in the housing. The housing is closed by a 
screw-plug, J. 

The gas acts on the end P' of the piston, and presses the 
knife into the copper disk, causing it to make a cut, whose 
length measures the pressure. A small copper cup, c, is 
placed at the outer end of the piston to act as a gas-check, 
and prevent the entrance of gas into the housing. This 
gauge, when used, is placed in the centre of the bottom of 
the cartridge-bag and tied to it with a string around the 


groove g. When in the gun, it must rest against the bottom 

Fig. 23. v. 

•of the bore. The gauge may also be screwed into the 
breech-block, or walls of the bore, 
in which case it is threaded on the 

Noble Crusher Gauge. — This ) 
has replaced the Rodman gauge gen- 
erally, for reasons which will appear 
later. It was used in Noble and Abel's 
experiments. It consists (Fig. 24) of 
a housing, H, closed by a screw-plug, 
/, and forming a receptacle for the 
working parts. 

These consist of a piston, P, mov- 
ing in a cylindrical channel as shown, 
and a copper cylinder, C, to be com- 
pressed, which is in contact with the 
piston. The cylinder is central, and 
kept in the axis of the housing by the 
spring S. 

A copper cup, c, is used as a gas- 
check as in the Rodman, and an- FlG - 24 ' 
■other method for the same purpose, called "air-packing," 

' LJ 




-' . 1 

LJ ' 

—a *> — 





L d i 









is also employed. A series of grooves, a (Fig. 25), are 
made around the piston. If gas enters between the piston 
and its channel, it escapes into the 
first groove, and by expanding, its ten- 
sion is diminished. It may also escape 
into the second groove, and so on, and 
by each expansion its tension is stiU 
FlG - 25- further reduced till it is unable to 

penetrate into the body of the housing. The action of the 
gauge is evident. In using it, the piston must always be in 
contact with the copper cylinder. 

Advantages of Noble Gauge. — 1. It is smaller than 
the Rodman, since the copper cylinder is smaller than»the 
disk. It therefore takes up less room in the gun. The mas& 
of the piston is also less than that of the knife and piston in 
the Rodman. 

The advantage of this has been shown. 

2. The knife of the Rodman is difficult to reproduce if 
broken,- while the piston of the Noble can always be dupli- 

3. The copper disk offers very little resistance to motion 
at first, while that offered by the cylinder is more nearly 

4. The cylinder can be given a preliminary compression, 
but a preliminary cut cannot be given to the copper disk. 

49. Determination of Pressures by the Dynamic Method — Noble and 
Abel's Method -Letard's Apparatus — Sebert's Velocimeter. 

In this method the pressure is determined by the accel- 
eration of a known mass. The mass may be either the pro- 
jectile, the gun, or a piston lodged in the walls of the bore, 
and communicating with it by a radial channel. 

Noble and Abel's Method. — In this method the mo- 
tion of the projectile is used, as already explained, page 77*. 
and the result is given by equation (150), 



the value of — being determined by calculation from data 

obtained by the experiment. 

Letard's Apparatus.— To avoid piercing the walls of 
the bore, as in Noble and Abel's method, this apparatus is 


Fig. 26. 

employed. It consists (Fig. 26) of a body of wood, on the 
front of which is a metallic ring, b. A metal bolt, a, passes 
through the wood body and projects to the rear, its head 
being in contact with the ring b. A pin, c, which is easily 
broken, holds the bolt a in place. When in this condition 
the current passes through the ring and bolt. 

The wood body is attached to a second piece of wood, 
and the whole is placed in the bore of the gun, and secured 
against the wall with resin or cement. When the projectile 
strikes the projecting end of the bolt a, the pin c is broken, 
and the bolt driven out, thus breaking the circuit. 

Sebert's Velocimeter.— With this instrument the mo- 
tion of the gun, or of the projectile, or of both, may be used. 
The general principles are as follows : A ribbon of steel 5 
(Fig. 27) is attached to the trunnion of the gun by the rod T 
and the gun mounted so as to recoil with very little friction. , 
As recoil takes place, the ribbon has the same motion as 
that of the gun. A tuning-fork, A, whose rate of vibration is 



known, is fixed, with reference to the gun, above the ribbon, 
and carries a quill-point, b. The fork is made to vibrate by 
electro-magnets, c, as in the Schultz Chronoscope, and dur- 
ing recoil the quill-point traces on the blackened surface of 
the ribbon a sinusoidal curve which is the scale of time. 
In rear of the tuning-fork are placed several Marcel-Deprez 
registers, R, connected with Letard interrupters in the gun. 
When the projectile passes a point at which one of the inter- 

Fig. 27. 

rupters is situated, the break is registered on the steel rib- 
bon beside the scale of time, and so for each successive 
break. The number of vibrations between breaks, divided 
by the number of vibrations per second of the fork, gives 
the time of passage of the projectile over the distance be- 
tween interrupters, and from this we can determine the 
velocity. From these velocities we can determine the ac- 
celerations, and hence the pressures, using the mass of the 

Since the ribbon contains a complete record of the mo- 
tion of recoil of the gun, we can also determine velocities 
and accelerations, and hence the pressures, using the mass 
of the gun. 




50. Definitions and Classification. 

An Explosive is a substance which is capable of a sudden 
change from a solid or liquid to a gaseous state, with evolu- 
tion of great heat. 

A High Explosive is one in which this change is very- 
rapid, and is accompanied by a crushing or shattering 

A Low Explosive is one in which the change is relatively 
slow, and accompanied by a propelling or pushing effect. 
Classification. — Explosives may be classed into 

i. Explosive mixtures ; 

2. Explosive compounds. 

Explosive Mixtures are intimate mixtures of certain sub- 
stances which are in themselves inexplosive, and which 
undergo no chemical change till the moment of explosion. 
They consist generally of a combustible body, such as car- 
bon, and an oxidizing agent, such as potassium nitrate. 
The best example is gunpowder, which has already been 

Explosive Compounds are chemical compounds, the mole- 
cules of which are explosive in themselves. They contain 
one or more combustible elements, such as carbon and hy- 
drogen, together with the oxygen necessary to oxidize these 

The constitution of the molecule is more or less unstable, 
and when heated to a certain degree, the molecule breaks 
up with the formation of the gaseous products of oxidation. 

The most important explosive compounds are the or- 



ganic nitrates or nitric ethers, whose composition may be 
represented by R-O-NO,, and the nitro-substitution com- 
pounds, represented by R-NO, , R in each "case represent- 
ing the'hydrocarbon radical. 

Both are derived from organic substances by the action 
of nitric acid, — the former from complex alcohols, such as 
glycerine, etc.; the latter from certain hydrocarbons, — by 
the substitution in each case of NO, of the acid # for H of the 
alcohol or hydrocarbon. 

Usually from each substance a series of explosive com- 
pounds can be made, depending upon the number of atoms 
of H replaced by NO,. 

In the explosive mixtures, relatively great distances exist 
between the atoms which are to combine, while in the com- 
pounds each molecule constitutes a complete explosive, 
and hence the transformation is much more rapid with the 

51. Orders of Explosion — Berthelot's Theory — Detonators. 

Orders of Explosion. — When gunpowder is fired in 
the ordinary manner we have an explosion of the second 
order ; when it is mixed with nitro-glycerine and fired, we 
may have an explosion of the first order, or a detonation. 

The difference consists in the time necessary to produce 
the chemical change. In the case of the explosion of the 
second order, the time is appreciable ; in the case of detona- 
tion the change is practically instantaneous throughout the 
whole mass of the body. 

Berthelot's Theory.— Berthelot, the great French 
authority, accounts for the difference in these orders as fol- 
lows : Every explosion is caused by heating some part of 
the substance to the temperature of decomposition, and 
this temperature is transmitted successively to all parts of 
the body. 

In the case of explosions of the second order, the portion 
of the substance first heated explodes ; but if the gases have 
space in which to expand, they are cooled to a certain ex- 
tent, and heat only a small additional portion of the ex- 
plosive body to the temperature of explosion. This new 


portion then explodes, and the cooling again takes place ; 
and so on, the explosion being propagated successively 
from layer to layer. This is the ordinary case with gun- 

Suppose, now, that a violent shock is given to any part 
of the explosive body, and that the pressures resulting from 
this shock are too great to be transmitted throughout the 
mass of the explosive. 

The energy of this shock will be transformed into heat, 
and this heat will affect the first layers of the explosive 
body and cause them to be suddenly converted into gas, or 
will produce detonation. This gas being suddenly pro- 
duced, the body causing the shock will not have time to be 
displaced, and therefore the expansion of the gas thus pro- 
duced will cause a new shock, more violent than the first, to 
the layers below. 

The energy of this shock will be transformed into heat, 
and will cause the second layer to detonate, and so on. 

Hence we have an alternate conversion of energy into 
heat and of heat into energy, and this conversion resembles 
the propagation of a sound-wave in a given medium, except 
that its rate of travel is much greater. We may also have 
a combination of these orders of explosion, so that the dis- 
tinction between the two cannot be sharply defined. 

Every explosive seems capable of producing the two 
different orders of explosion, according to the manner in 
which the initial heating or shock is given. The high ex- 
plosives give ordinarily the first order of explosion, the low 
explosives the second order. 

Detonators. — The order of explosion generally de- 
pends on the intensity of the initial shock. If this is not 
great enough, the explosive may burn quietly, or give an 
explosion of a lower order. To produce this initial shock, 
a small quantity of some violent explosive, called a detona- 
tor, is required. 

The principal detonating agent in use is fulminate of 
mercury, which, on account of its great force, gives rise to a 
high temperature when the initial shock is converted into 



52. Modes of Producing Explosion — Fuzes — Detonation by Influence. 
An explosion of the second order may be produced by 
shock, friction, the direct application of heat, by electricity 
or by an ordinary primer, and by certain chemical or physical 
changes; but to produce. detonation a special fuze, called a 
detonating fuze, is generally employed. The material used in 
these fuzes is ordinarily mercuric fulminate,and one 
form is shown in Fig. 28. A is a copper shell ; B, 
the chamber filled with mercuric fulminate ; C, 
the electric wires ; D, the ends of these wires ; E, 
D the platinum bridge which is heated by the cur- 
rent ; F, the sulphur cement holding the wires and 
fulminate in place. This fuze is placed in the 
mass of the explosive, as its effect is weakened if 
a layer of air is interposed. Other varieties of 
fuzes are used. Those fired by electricity are 
-Q classed as high and low tension, according to the 
kind of current used with them. 

Mass of Fuze. — The mass of the detonator 
should bear a certain proportion to that of the 
explosive. If it is too weak, it produces a low 
order of explosion ; if too strong, it may scatter 
the explosive. 

The exception to the rule is nitro-glycerine, 
which detonates equally well with a small or a 
large primer'; but it holds for gun-cotton, and for 
those explosives which have been rendered less 
sensitive by various means. 
3 - Detonation by Influence. — If a series of 

cartridges of dynamite or gun-cotton be placed at certain 
distances apart, and one of them be detonated bv a fulminate 
primer, the others will also detonate. This is called " deto- 
nation by influence" or "sympathetic" detonation. It ap- 
pears to be governed by the following laws : 

1 The distance apart at which detonation occurs de- 
pends on the envelope of the cartridges, and the nature of 
the material on which the cartridges rest. If the initial 
cartridge is enveloped in a non-resisting material, such as 
a paper envelope, the influence extends much further than 



with a resisting envelope. If the cartridges rest on a re- 
sisting material, as an iron rail, the effect is propagated to a 
greater distance than if they rest upon the ground. 

2. The envelope of the secondary charges should be as 
thin and elastic as possible, in order to oppose the minimum 
resistance to the shock. 

3. An explosion thus propagated will become weaker 
from cartridge to cartridge, and may even change its order. 

4. Similar effects are observed under water. 

5. The shock is better transmitted by a liquid than by a 

6. The density of the secondary charges should be as 
great as possible, in order that the effect may not be reduced 
by motion among the particles. 

53. Strength of an Explosive — Potential — Force — Bapidity of 

Strength.— An explosive must be considered as exert- 
ing pressure and having potential energy, and in order to 
estimate its strength, and its value for different purposes, 
we must be able to determine the relative values of the pres- 
sure and potential for each explosive. 

Water in freezing exerts great pressure if confined, and 
may burst the walls of the containing vessel. The frag- 
ments, however, will not be projected to an}- distance. 

In this case we have a great pressure, but no potential 
energy or capacity to do work. If instead of water a high 
explosive be confined in the envelope and detonated, two 
effects will be observed : the walls will be ruptured, and the 
fragments thrown violently in all directions. In this case 
we have the pressure required to rupture the walls, and the 
potential energy necessary to project the fragments. 

Again, if we compare equal weights of large and small 
grained powder of the same composition, exploded in a 
closed vessel, it is evident that the potential is the same for 
both, since the products and the quantity of heat dis- 
engaged are the same ; the force or pressure is also the 
same, since this depends solely on the density of loading. 
The effect of these powders is, however, very different. 


The small-grained powder, if exploded in a shell, will 
burst it into many fragments and project them to great dis- 
tances, while the large-grained powder will give few frag- 
ments and small propelling force. Similar effects are ob- 
served with different classes of high explosives, and depend 
on the rapidity of the reaction by which they are converted 
into gas. 

The strength of an explosive, then, depends on — 

i. Its force or pressure ; 

2. Its potential ; 

3. The rapidity of its reaction or conversion. 

Force or Pressure. — The force of an explosive, as 
already defined in the case of gunpowder, is the pressure ex- 
erted by its gaseous products per unit of surface, when unit 
weight of these products is confined in unit volume. The 
expression for it in the case of gunpowder is, equation (28), 

J ~ 273 ' 

and the same expression measures the force of any explosive, 
v t being the specific volume, p the atmospheric pressure, 
and T a the absolute temperature. 

Potential. — The potential energy of an explosive is the 
total work it can do, when the products are indefinitely ex- 
panded without loss of heat, all the heat being expended in 
the performance of work. 

Let E be the potential energy of unit weight of the ex- 
plosive, J the mechanical equivalent of a heat-unit, T a the 
absolute temperature of explosion, and K the mean specific 
heat of the products. Then 

E = KTJ. 

Rapidity of Reaction. — This depends on the rapidity 
with which the chemical transformation is propagated 
throughout the mass of the explosive. Certain explosives, 
such as nitro-glycerine and gun-cotton, have very great 
velocities of conversion, and the}- may be regarded as un- 
dergoing an instantaneous change. 


This change being so rapid, the heat is employed almost 
entirely in expanding the gases and performing mechanical 
work. Hence these substances are violent explosives, and 
shatter everything in their path. 

The transformation is made to take place less rapidly by 
removing the particles to a greater distance from each other, 
as in the case of gunpowder, which then decomposes com- 
paratively slowly and exerts a pushing effect rather than 
that of a blow. 

It is evident that the choice of an explosive depends upon 
the relative values of these three elements. If an explosive 
is required for a shell, we need one having the greatest pos- 
sible potential to scatter the fragments, a relatively small 
force, so as not to break it into very small fragments, and 
great rapidity of reaction in order that all the gases may 
be formed before the shell breaks. For mining, we require 
moderate force, small potential, and moderate rapidity of 
reaction, etc. 

54. Principal Explosives — Gun-cotton. 

Principal Explosives. — Gunpowder may be regarded 
as a type of the explosive mixtures, and as its properties are 
possessed to a greater or less extent by all these mixtures, 
the high explosives only will be considered in what follows. 

The principal ones in use for military purposes are : 

i. Gun-cotton; 

2. Nitro-glycer ine; 

3. Dynamites; 

4. Picric acid and picrates ; 

5. Fulminates ; 

6. Sprengel safety mixtures ; 

7. Smokeless powders. 

Gun-cotton. — Its chemical formula is C„H,0,(ONO,)„ 
and it is formed from cotton wool by the action of strong 
nitric acid. The reaction is 

C„rLO,(OH) s + 3HNO3 = CHAfONO,), + 3 H a O. 

Cellulose. Nitric Acid. 

Sulphuric acid is added to the nitric to take up the water 
and prevent the dilution of the later acid, which would give 


the lower orders of nitration, such as collodion cotton. The 
method of preparing it is described in chemistry. 

In the earlier processes of manufacture the long fibres 
of cotton were used. These became filled with the acids, 
and being capillary tubes, it was found impossible to wash 
them out, and hence the product was unstable and liable to 
spontaneous decomposition. Abel, however, improved the 
process of manufacture by selecting the cotton waste, and 
cleaning it with alkaline washing, and especially by cutting 
up, or pulping the gun-cotton after it had been partially 
freed from the acids employed in its manufacture. By this 
operation the long fibres were reduced to very short tubes 
which could be thoroughly washed. A final washing in 
alkaline water completed the neutralization of free acids. 

Forms. — Gun-cotton occurs ordinarily — 

i. In the form of wool, like the original cotton; 

2. In compressed cylinders and slabs. 

The first form is that in which the cotton was used up to 
the time of Abel's improvement. It was sometimes twisted 
into strands, and woven, to regulate its rate of burning. 

The compressed cylinders are made by the action of a 
hydraulic press upon the pulped and washed gun-cotton. 

Properties — Density. — Its density is about 0.2 for the wool 
form and 1.1 for the dry compressed. 

Solubility. — It is insoluble in water, alcohol, or sulphuric 
ether, but is soluble in acetone and acetic ether. This in- 
solubility in alcohol and sulphuric ether distinguishes it 
from the lower orders of nitrated cellulose, which are soluble, ' 
giving collodion. 

Effect of Foreign Substances. — The addition of water de- 
creases the sensitiveness to explosion. The addition of 
paraffine has a similar effect, with the advantage that it does 
not evaporate. The reason for this decrease in sensitiveness 
is that the water or paraffine gives a certain elasticity and 
solidity to the gun-cotton, so that the initial shock of the 
detonator is propagated through a much greater mass, and 
consequently its local energy is diminished. 

Nitre is sometimes added to increase the supply of 
oxygen, which is deficient. 


Free Acids. — These cause spontaneous decomposition, 
with elevation of temperature and increased sensitiveness, 
so that explosion frequently results. 

The presence of these acids formerly caused many acci- 

Effect of Heat and Cold. — As a general rule, the sensitive- 
ness of a high explosive increases with the temperature. If 
wet, the application of heat will cause the evaporation of the 
water and thus increase the sensitiveness of the gun-cotton. 

Cold will cause the freezing of the wet compressed gun- 
cotton and its consequent flaking and disintegration. 

Ignition. — A temperature of about 180 C. is required. 
If the cotton is dry and unconfined, the application of flame 
will cause it to burn quickly. If the mass is large, an explo- 
sion may occur, but it will be ordinarily of a low order. If 
wet, the cotton will burn when unconfined, only in successive 
layers as they become dry. 

Detonation. — Dry gun-cotton is detonated by a fulminate 

Wet or paraffined gun-cotton requires a large detonator or 
an initial priming charge of dry cotton with a fulminate fuze. 

Reaction, — The reaction on explosion is 

2C,H 7 0,(ONO J ), = 7H,0 + 3 CO, + 9 CO + 6N. 

There is evidently a deficiency of oxygen, and hence of 
potential energy, and therefore nitre is sometimes added as 
before stated. 

Use in Blasting. — From the CO given off it is disadvan- 
tageous in blasting unless a nitrate be added. It has also 
the disadvantage of being of comparatively low density and 
solid, and hence it cannot be introduced so readily into bore- 
holes, nor in such large quantities as other explosives which 
are plastic or have higher densities. It is, however, very safe. 

Use for Military Purposes. — It has been used for charging- 
torpedoes, for bursting charges for shell, and for destroying 
obstacles such as walls, palisades, guns and carriages, etc. 

Storage. — It is best stored wet, as under these conditions it 
is perfectly safe. It should not, however, be exposed in this 
state to a freezing temperature on account of disintegration- 


55. Nitro-glycerine. 

Its chemical formula is C S H S ' C)NO,\ , and it is formed by 
the action of strong nitric acid upon glycerine. 

The reaction is 

C a H 6 (OH) 3 + 3 HNO a = C 3 H 6 (ONO,) 3 + 3 H,0. 

Glycerine Nitric acid 

Sulphuric acid is added to the nitric, as in the case of 
gun-cotton, to take up the water formed in the reaction. 

The method of preparing it is to add the glycerine slowly 
to the mixture of acids ; to keep the mixture cool by cooling 
coils in the vessel, and by passing a current of air through it, 
which also insures a thorough mixture ; and to wash the pro- 
duct thoroughly with water to which a small quantity of 
alkali is added, to insure the removal of free acid. 

Form. — Nitroglycerine when first made is in the form of 
an opaque, white, oily liquid, becoming colorless with time. 

Properties — Density. — Its density is 1.6. 

Solubility. — It is very slightly soluble in a large quantity 
of cold water. It is freely soluble in alcohol, ether, chloro- 
form, and slightly in glycerine. 

It has a sweet, pungent, aromatic taste ; is poisonous, and 
causes headache. 

Heat and Cold. — It freezes at4°.4C. to a white crystalline 
solid, and is almost inexplosive in this condition by ordinary 
means, unless a small mass be acted upon by a shock. 

When frozen, it is thawed at a temperature of 37 . 7 C. by 
placing the vessel containing it in another of water at this 

Free Acids. — These cause its decomposition, as in the 
case of gun-cotton, and render it more sensitive to friction 
and percussion, and hence they must be carefully removed. 

Ignition. — Its temperature of ignition is about the same 
as that of gun-cotton, 180° C. 

If unconfined and subjected to a blow, the particle struck 
will explode, and scatter the remainder. 

If confined and struck, it will detonate ; when unconfined, 
in small masses, the application of flame causes it to burn 
rapidly without explosion. 


Detonation. — It is detonated by mercuric fulminate, and 
the detonator should be placed in the liquid. If frozen, it 
may also be detonated, but the action is generally less 
violent, owing to incomplete conversion. 

Reaction. — The reaction on explosion is 

2C 3 H 6 (ONO a ), = 6CO, + 6N + 5 H,0 + O. 

Here we have an excess of oxygen, and the reaction, 
following a general law, is always stable. 

Use in Blasting. — Nitro-glycerine is one of the strongest 
of the high explosives, possessing great force, potential, and 
rapidity of reaction. Owing to its liquid form it can be 
poured into holes of any shape, provided they do not com- 
municate with fissures, and from its great rapidity of re- 
action, the depth of the hole may be decreased, and no tamp- 
ing except water is required. It is therefore a valuable 
agent for blasting, but owing to its liquid form it is very 
unsafe in handling, as it is liable to leak, and thin films of it 
may be easily exploded. For this reason, except for special 
purposes, it is now generally replaced by dynamite. 

Use for Military Purposes. — The same remarks apply in 
this case as for blasting. 

Storage. — If possible nitro-glycerine should be kept frozen, 
and should be transported and handled in this state, being 
thawed before using. 

Test for Purity. — Free acid may be detected by using blue 
litmus-paper. The acid will redden it. 

56. Dynamite — With Inert Base. 

Owing to the dangers involved in the transportation, 
handling, and storage of nitro-glycerine as previously noted, 
efforts were made to find an absorbent for it, so that it could 
be given a solid form. The addition of these absorbents has 
given rise to dynamite and various other derivatives of 

Absorbents Classified. — These may be classified into: i. 
Inert; 2. Chemically active. 

Inert Absorbents — Dynamite No. i. — The most im- 
portant of the inert bases is kieselgiihr, a siliceous infusorial 


earth which is porous, and will absorb and retain about three 
times its weight of nitro-glycerine. 

When it absorbs about 75 per cent of nitro-glycerine, the 
product is called dynamite No. 1. 

Form. — It is either granular, or in compressed cylinders,, 
wrapped in paraffined paper. 

Properties — Density. — Its density is about 1.5 to 1.6. 

Heat and Cold. — Dynamite freezes at 4°.4C, and in this- 
condition is detonated with great difficulty when solid, but 
when loose it may be detonated, the explosion being less 
violent. If frozen, it must be thawed before exploding, and 
this should be done very carefully, as in common with all 
preparations of nitro-glycerine it becomes more sensitive as 
it is heated. At all high temperatures the nitro-glycerine 
exudes, and hence the dynamite becomes dangerous. 

Free Acids. — These are very dangerous, and the same re- 
marks apply as to nitro-glycerine. 

Detonation. — A fuze of fulminate of mercury is used, which 
must be placed in the mass of the cartridge. 

Reaction. — This is the same as for nitroglycerine. 

Use in Blasting. — It has been found very useful in blasting 
on account of safety in handling. The potential is dimin- 
ished by the presence of the silica, and hence its action is 
less violent, and its effects more distributed. By regulating 
the percentage of nitro-glycerine present, this effect may be 
still further modified. 

Use for Military Purposes. — In the U. S. service, Dynamite 
No. 1 is used for charging torpedoes, and may be regarded 
as the standard high explosive for this purpose. General 
Abbott of the U. S. Engineers has made a series of researches 
upon 'this subject, and has deduced formulas for the inten- 
sity of different explosives when used under water. (See 
" Professional Papers, Corps of Engineers," No. 23 — 1881.) 

Storage. — Dynamite No. 1 is stored in boxes of wood, in 
magazines free from dampness, and no fulminate caps or 
primers should be stored with it. 

57. Dynamite with Chemically Active Bases. 

Instead of an inert base, a combustible one may be used, 


Avhich is capable of combining with the excess of oxygen of 
the nitro-glycerine and thus increasing the potential. 

Various substances have been used for this purpose. 

90 per cent of nitro-glycerine and 10 per cent of charcoal 
form carbo-dynamite. Sawdust, treated with superheated 
steam, becomes a jelly, and is capable of absorbing a large 
quantity of nitro-glycerine. Other compounds of the same 
class are also found. 

On the other hand, by using a nitrate or chlorate mixture 
as a base, additional effect is obtained by inducing a higher 
order of explosion in the base. When gunpowder is used 
as an absorbent, the detonation of the nitro-glycerine causes 
the detonation of the powder. Potassium-chlorate mixtures 
are also used for this purpose, but are generally regarded as 

High Explosive Bases. — The most important of these com- 
pounds is explosive gelatine or " gum-dynamite." 

It has been shown that when gun-cotton detonates, there 
is a deficiency of oxygen, and in the case of nitro-glycerine 
there is an excess of it. 

If these two explosives are mixed in such proportions as 
to have the excess of oxygen in the one, neutralize the defi- 
ciency in the other, we have a considerable increase of 
potential. The result is best realized in a substance called 
explosive gelatine or gum-dynamite, which was invented by 
the Swedish engineer Nobel. 

It is made by dissolving 7 parts of a special grade of 
soluble gun-cotton in 93 parts of nitro-glycerine, by the aid 
of heat. 

For military purposes about 4 per cent of camphor is 
added to decrease its sensitiveness. 

Form. — It is a translucent jelly of a yellowish or dark 
brown color, which may become in time hard and opaque. 

Properties — Density. — Its density is 1.6. 

Solubility. — It is insoluble in water and is unaffected by 

Heat and Cold. — If heated slowly to 204° C, it explodes ; 
and it freezes at low temperatures. 

Ignition. — When ignited unconfined it burns readily, but 


does not explode ; but if confined, explosion occurs. It is not 
affected by shock, and bullets have been fired through it 
without producing explosion. 

Detonation. — For detonation a special primer is required, 
and the strength of the primer must be increased as the 
sensitiveness of the gelatine is decreased. 

Use for Military Purposes. — It has been tried as a bursting 
charge for shells ; but as it requires a large primer, the ad- 
vantages of the decrease in sensitiveness of the explosive 
are lost by the increase of sensitiveness of the primer. 

Storage— Some doubt exists as to the stability of this 
compound, and the effect upon its sensitiveness of the evap- 
oration of the camphor. 

58. Picric Acid and Picrates — Fulminates. 

The chemical formula for picric acid or tri-nitro-phenol 
is C e H 2 (NO a ),OH, and it is formed by the action of nitric 
acid on carbolic acid. The reaction is 

C,H s OH + 3 HN0 3 = C 6 H,(N0 2 ) s OH + 3 H.O. 

Form. — It occurs in yellow crystals which are slightly 
soluble in water. It explodes when heated rapidly, but is. 
ordinarily not used as an explosive by itself, and is only of 
importance from its compounds. 

Potassium Picrate. — This salt is a violent explosive. 
Mixed with nitre and charcoal and grained, it forms Desig- 
nolle's powder, which has been used for small arms and 
cannon, and also for torpedoes, with good results, but it is 
expensive, and some cases of premature explosions have been 

Ammonium Picrate. — This is less sensitive than the potassa 
salt, and burns without explosion in the air. Mixed with 
nearly equal parts of nitre, it forms Brugere's powder, which 
has about twice the strength of ordinary gunpowder, but is 
expensive, somewhat hygroscopic, and too violent for small 

The picrates form the bases for certain smokeless 

Emmens Acid. — This acid is said to be formed by the- 
action of nitric acid upon picric acid. 


Emmensite is a mixture of emmens acid and sodium or 
ammonium nitrate. It is yellow and crystalline in appear- 
ance, and is used in mining and as a substitute for gun- 
powder, both as a propelling agent and for charging shells. 
It is much stronger than gunpowder, is smokeless, and 
almost insensitive to shock. 

It is hygroscopic, and its stability after long storage is 
not yet well settled. It was invented by Dr. Emmens, and 
is sti!l undergoing trial. 

Melinite. — This French explosive is generally supposed 
to be a mixture of gun-cotton with picric and cresylic acids 
dissolved in ether. 

Fulminates. — The most important is mercury fulminate, 
the chemical formula for which is HgC,N 2 2 . It is formed 
by the action of alcohol upon mercury nitrate. The reac- 
tion is rather complex, and may be found in the chemistry. 

Form. — It is in fine gray crystals. 

Properties — Density. — Its density is 4.42. 

Solubility. — It is insoluble in water, not affected by the 
air, and is poisonous. 

Water. — When saturated with water it is inexplosive, 
and hence it is always kept under water for safety. 

Detonation. — When dry it is very sensitive to a blow and 
detonates with violence, and also when heated to 182 C. 
or when subjected to friction, or to contact with any ignited 
body, or to the action of the electric spark. 

Reaction. — The reaction on explosion is 

HgC,N,0, = Hg + 2CO + 2N. 

Use. — The great value of this explosive is as a detonator 
for the other high explosives. Its effects are due to its great 
force, since the volume of gas given off is very great ; and 
also to its high density, in consequence of which a large 
mass is contained in a small volume. The gases also are 
not subject to dissociation, and hence impart all their energy 
to the explosive to be detonated. It is said to have ten 
times the force of gunpowder. Being comparatively low 
in potential, an oxydizing agent is sometimes added when 
the primer is at a distance from the charge. 


Storage. — It must be kept under water for safety, and 
irnust not be allowed to come in contact vrith a metallic sur- 
face, as it then tends to decompose. Hence percussion-caps 
are varnished before it is placed in them. It must not be 
stored with high explosives. 

.59. Nitro-Beazines — Sprengel Safety Mixtures. 

Nitro-benzines. — These are formed by the action of 
nitric acid on benzine, and we have the mono-, di-, and tri- 
Jiitro-benzines resulting. 

They are not explosive, but are used in the manufacture 
of a class of explosives called Sprengel safety mixtures. 

Sprengel Safety Mixtures. — These were invented by 
Dr. Sprengel ; the idea being to mix an oxydizing with a 
combustible agent at the time it is to be used, the constituents 
being each non-explosive before mixture, and therefore safe 
to handle and transport. 

Rack-a-rock is a Sprengel mixture of liquid mono-nitro- 
benzine and potassium chlorate. If the cartridges are kept 
awhile, their sensitiveness to friction or percussion increases. 
This explosive was used at Hell Gate in 1885 ; 240,000 lbs. 
■of it being exploded together with 42,000 lbs. of dynamite. 

Hellhoffite is a mixture of di-nitro-benzine and nitric acid. 
It lias been used as a bursting charge for shells, by plac- 
ing the components in separate vessels in the shell, and caus- 
ing their mixture automatically, either during its flight or on 

Bellite is a mixture of tri-nitro-benzine with ammonium 
nitrate. It is not sensitive to blows or friction, is chemically 
stable, and can be stored and transported without change or 

Another class of explosives of the same kind are the 
flameless explosives, which when confined and detonated, 
■evolve gases which quench any flame. They are especially 
wseful in mines where fire-damp is prevalent. 

Roburite is one of the class of flameless explosives, made 
by mixing ammonium nitrate and chlorinated di-nitro*bem>- 
zine, and is a yellowish powder. It is flameless because the 
ingredients are so proportioned as to cause complete oxida- 


tion, and the products of combustion are carbon dioxide, 
water, nitrogen, and HC1; the gases given off quenching any 
flame that may be produced. 

Many other explosives of this class are made, and their 
composition may be found in " The Dictionary of Ex- 
plosives," by Major J. P. Cundill. 


60. Changes in Black Powders — Early History of Smokeless 

Changes in Black Powders.— A general idea has been 
given previously of the history of gunpowder, and the 
changes made in it. It was found to be too strong even for 
modern guns in the small-grained form, and hence Rodman 
conceived the idea of suiting the grain to the calibre. 

His perforated powder was also designed with the idea 
of burning on an increasing surface, and thus decreasing the 
volume of the gas emitted at first, and hence the maximum 

No change had been made in the components of the 
powder. Later still these changes in form were combined 
with changes in the nature of the materials, and their pro- 
portions. In the cocoa-powder the nature of the charcoal 
was changed, as were also the proportions of nitre, sulphur, 
and charcoal, and certain carbo-hydrates were introduced. 

While these changes made the powder slower, they 
necessitated larger charges. This increased the cost, oc- 
cupied a greater volume of bore, and thus reduced the path 
over which the gases worked, and necessitated long bores, 
and also gave great volumes of smoke. 

With small arms, when the calibre was reduced to 0.30, 
the length of the bullet remaining the same, it became neces- 
sary, in order to obtain an increase in velocity, to increase 
the mean pressure per unit of area of the projectile, and 
hence to adopt some agent having better ballistic qualities 
than the old powders. Increased charges of compressed 
black powders were first tried, but they gave high and 


irregular pressures and relatively lower velocities than with 
the old charges. 

Early History of Smokeless Powders. — To obviate 
these defects a new explosive was sought, which would in- 
crease the velocities, without increasing the pressures beyond 
safe limits. Naturally the high explosives were tried, and 
of these the most promising was gun-cotton. It was known 
that this gave no smoke, that it burned freely when uncon- 
fined, but that it detonated when confined. Attempts were 
therefore made to regulate its burning, by twisting it into 
strands and winding these on the exterior of a hollow wood 
cylinder, so that the cartridge thus made would fit the 
chamber of the gun. It was supposed that when sufficient 
pressure was developed, the cylinder would crush, and thus 
give a very much larger volume for the gases to expand in, 
and hence prevent detonation. It was found, however, that 
detonation did occur, with destruction of the gun, and 
attempts in this direction were abandoned. 

Another method was to mix gun-cotton with ordinary 
cotton. The two were after mixture subjected to a strong 
compression, but it was difficult to obtain a homogeneous 
mixture, the velocities were not increased, and the gun- 
cotton still detonated. 

An attempt was also made to place a charge of black 
powder in front of the charge of gun-cotton. The projec- 
tile was started by the burning of the black powder, and 
then the gun-cotton was inflamed. 

This plan gave excessive pressures in practice, and was 
soon abandoned. 

Abel's compressed cotton was also tried with the same 
results, and gun-cotton was then abandoned as a propelling 
agent. This was about 1884. 

61. Modification of Gun-cotton — Effect of Calibre. 

Modification of Gun-cotton.— In all the early trials 
of gun-cotton no essential modification of its physical con- 
dition was attempted. 

• The fibres of the gun-cotton were not compact, and on 
being subjected to the action of a highly-heated gas, the 


flame readily penetrated all parts of the mass, raising it to 
the temperature of explosion, and detonation followed. 

In 1884 it was proposed to dissolve the gun-cotton in 
some solvent, which could afterwards be evaporated, leav- 
ing a compact horny substance, which would resist the 
penetration of flame, and burn regularly. This was the 
first step in the successful manufacture of smokeless powder. 

Effect' of Calibre. — With black or nitrate powders, as 
has been shown, the size of the grain must increase with the 
calibre for all large guns, but for all small arms the same 
powder (small-arms) may be used with good results. 

With smokeless powders, however, each change in 
calibre of the small arm requires a change in the powder 
used. This may be explained as follows : As the calibre 
decreases, the length of the bullet remaining constant, while 
its weight decreases, it is necessary to increase the initial 
velocity of the projectile to obtain superior ballistic results, 
and this increase of velocity can only be obtained by an in- 
crease of pressure per square inch of the powder-gas. 

To obtain this increase the physical qualities of the 
smokeless powder are modified so as to obtain a quicker 
powder, and this is accomplished by stopping the solution 
of the cotton at the proper point, and by decreasing the 
thickness of the grain. For the larger calibres the solution 
of the cotton is more complete and the grains thicker. 

Those physical qualities, therefore, which principally 
affect the velocities and pressures given by the powder are : 

1. Its degree of solution or density ; 

2. Its thickness, or least dimension of grain ; 
both of which regulate its burning. 

In order to increase the pressure per unit of area, a 
proper combination of these qualities is required for each 
particular calibre, and this requires a special powder for 
each gun. 

62. Operations in the Manufacture of Smokeless Powder — Solution. 

Operations. — The principal operations in the manufac- 
ture of a smokeless powder of the nitro-cellulose class are : 

1. Preparation of the nitro-cellulose; 


2. Solution of the nitro-cellulose in a proper solvent ; 

3. Compression of the material after evaporation of the 
solvent ; 

4. Rolling into sheets or pressing into rods or tubes ; 

5. Cutting up the sheets, rods, or tubes into grains ; 

6. Drying the grains. 

Solution. — The principal precautions to be taken in 
this operation are, to avoid the formation of lumps or undis- 
solved particles of nitro-cellulose ; to have the solvent act 
regularly ; and to prevent the cotton from collecting in 
masses, so that the solvent cannot readily penetrate it. If 
the powder is to be quick, the cotton must not be com- 
pletely dissolved, and hence the operation must be stopped 
at the proper time, which requires great delicacy in manip- 

In the operation, the gun cotton must not be plunged 'in 
the solvent, but the latter must be poured over the cotton. 
For this purpose the cotton, which is finely divided, is 
placed in layers of the proper thickness, in ebonite pans of 
slight depth. These are enclosed in a glass vessel, and the 
solvent added in the form of a spray. The gun-cotton 
gradually dissolves, or rather becomes gelatinized ; the sup- 
ply of the solvent is then stopped, and the solution allowed 
to proceed to the proper degree. A current of warm air is 
then passed over the gelatinized gun-cotton, carrying off the 
solvent in a state of vapor, which is afterwards condensed 
in a cool vessel. In this manner the drying of the powder 
is assisted, and the solvent which is removed can be used 
again. The cost of these powders depends principally 
upon the solvent, and hence it is important to collect as 
much of it as possible. 

63. Compression and Rolling — Cntting Tip — Drying. 

Compression. — During the evaporation of the solvent, 
bubbles are formed, the effect of which is to render the 
mass more or less porous in places. This causes irregular 
' density, and hence in the same sheet some parts would burn 
more quickly than others. It is necessary, therefore, to 
get rid of these bubbles. 


The thickness of the sheet, after the solvent has evapo- 
rated, is not uniform, as it is impossible to spread the cotton 
regularly before it is acted on by the solvent. This thick- 
ness is very important, as affecting the ballistic properties of 
the powder. • 

To get rid of the bubbles and at the same time regulate 
the thickness, the sheet is subjected to strong pressure, 
which is kept up for some time. This pressure has also the 
effect of completing the solution of certain parts which were 
not completely dissolved. 

Rolling. — The sheet is then passed between two rolls of 
polished bronze. The upper roll must be so arranged that 
its weight will not rest upon the sheet. In this way when 
the sheet has reached its proper thickness it will not be 
reduced further. 

The reduction to the required thickness is gradual, so as 
not to tear the surfaces. In general three or four successive 
passes through the rolls are necessary. 

Cutting Up. — Black powder is grained, but this opera- 
tion is impossible with smokeless powder, which is tough 
and flexible and cannot be broken. It is therefore cut into 
the required form by special machines, or pressed, while still 
pasty, through holes in a die, thus forming strings or cords. 

Drying.— The sheets are cut while still saturated with 
the solvent, and the drying accomplished after the powder 
is reduced to grains. 

This operation should take place slowly, and at a rela- 
tively low temperature. Without this precaution there is 
danger of evaporating the remaining solvent too rapidly, 
which would cause disintegration of the material and in- 
crease the porosity. 

Smokeless powders are difficult to dry, especially when 
thick, and hence when considerable thickness is required, as 
with cannon-powder, several thin sheets previously dried 
are placed on each other, and the whole compressed to the 
required thickness by hydraulic pressure. 

The drying should not be complete, a certain quantity of 
the solvent being left ; as in the case of black powders, a 


certain quantity of moisture is retained. This tends to di- 
minish the pressure and to keep up the normal velocity. 

The great difficulty in the manufacture of smokeless 
powder has been to make it in large quantities by machinery, 
so tWt it shall give uniform results as to velocity and pressure. 
It is not difficult to make small quantities in a laboratory, 
but very difficult to reproduce them on a large scale. 

64. Classification of Smokeless Powders — Classes 1, 2, and 3 — Wet- 
teren Powder. 

The manufacture described above applies only to the 
nitro-cellulose classes of smokeless powders ; but as the 
others are generally mixtures of different substances, in the 
state of powder, their preparation resembles that of gun- 
powder and requires no special description. 

Classification. — Smokeless powders are generally 
classed as: 
• i . Those derived from picric acid and the picrates ; 

2. Those derived from ammonium nitrate ; 

3. Those derived from nitro-cotton or from mixtures of 
nitro-glycerine and nitro-cotton, with the addition of cer- 
tain agents which act to modify the rate of burning. 

Class 1. Picric-acid Powders. — Of these Designolle's and 
Brugere's powders have already been described. This class 
is no longer of much importance, as it has been abandoned 
for powders of class 3. 

Class 2. Ammoninnunitrate Powders. — The objection to 
this class of powders is that they are all highly hygroscopic, 
and they are no longer used. 

Class 3. There are a few well-known powders of this class. 
Very little is known about their actual composition, and 
hence only a general description of them can be given. 

Wetteren Powder. — This is made in Belgium. It is 
said to be composed of nitro-cotton dissolved in acetic ether, 
with the addition of nitrate of baryta. Another composition 
given is nitro-cotton dissolved in acetic ether, with the 
addition of nitro-mannite, which is formed by the action of 
nitric acid on manna-sugar. The grains are hard, square in 
form, and of a slate color. 


To protect it irom moisture the grains are varnished 
with a special collodion. 

The defects of this powder are, it is expensive ; the acetic 
ether does not thoroughly dissolve the nitro-cellulose ; and 
after the solvent is evaporated, white scales are formed on 
the surface. In time this powder loses its compact struc- 
ture, and under the influence of shock reduces to dust in the 
cartridge-case, and this dust will cause excessive pressures. 
Also the acetic ether is difficult to evaporate, and hence 
different parts of the powder may contain different amounts 
of the solvent, and this gives rise to irregular ballistic quali- 
ties. This powder is now being tried in the U. 8. cal. 30 
rifle, charge 37 grains, muzzle velocity 2000 ft. -sees. 

65. Powder B. N. F.—Ballistite— Cordite. 

Powder B. N. F. — This powder is used in France in the 
Lebel rifle. Its composition is unknown, but it is supposed to 
be a mixture of cottons of different degrees of nitration, gela- 
tinized by suitable solvents. It is first formed into plates, 
these are rolled into sheets, which are cut up into grains for 
small arms or into strips for large guns. It has a grayish or 
yellowish color, is difficult to ignite, and is said to be very 
regular in its action and not affected by change of climate. 

BALLISTITE. — This powder is used in Germany and Italy, 
and is the invention of Alfred Nobel. It was the first success- 
ful smokeless powder made by uniting nitro-glycerine and 
nitro-cellulose. By acting upon a soluble gun-cotton with 
nitro-glycerine in the proportions previously given, Nobel 
produced explosive gelatine. By increasing the proportions 
of the nitro-cellulose to 30 or 40 per cent and reducing the 
nitro-glycerine to 60 or 70 per cent, the resulting mixture 
becomes a horny compact mass capable of definite granula- 
tion. About 7 per cent of camphor dissolved in the nitro- 
glycerine is found to assist the process. In the manufacture, 
benzole is mixed with the nitro-glycerine, to render the 
nitro-cellulose temporarily insoluble in order to facilitate 
its equal distribution and absorption. The benzole is then 
evaporated and the material repeatedly passed through 
steam-heated rolls and made into sheets. These are after- 


wards cut up into cubical grains which are dark brown in 
color and are horny and translucent when cut. It has about 
three times the ballistic force of black powder, and its effects 
are very regular. 

Cordite. — This powder is used in England and is the 
invention of Sir F. Abel and Professor Dewar. It is very 
similar to ballistite, except that a highly nitrated gun-cotton 
is used. 

As this is insoluble in nitro-glycerine, to obtain a stable 
union with the latter it is necessary to dissolve the gun- 
cotton in a solvent. Acetone is used. Various slowing 
agents have been tried. Tannin is called for in the patent, 
but at the present time about 10 or 15 per cent of vaseline 
is preferred. 

These powders are perfectly smokeless, and give high 
velocities with safe pressures. They are said to deteriorate 
rapidly, the manufacture is dangerous, and in some samples 
the nitro-glycerine exudes, rendering the powder sensitive. 
They give great heat on explosion, and this may, it is 
thought, injuriously affect the bores of guns. They are also 
difficult to explode. 

66. Leonard Powder — Peyton Powder. 

Leonard Powder. — This is an American powder whose- 
composition is gun-cotton dissolved in acetone, a large per- 
centage of nitro-glycerine, and a slowing agent. 

In shape it resembles cordite for large guns, the diam- 
eter of the cord increasing with the calibre of the gun. For 
small arms the cords are very small, and are cut in short 
pieces, so that the powder is granular in appearance. 

This powder has given good results in proof, and it is. 
now undergoing trial. The grains are rather soft. 

Peyton Powder.— This is also an American powder,, 
manufactured by the California Powder Works. It is a 
gelatinized mixture of nitro-glycerine 38 per cent and gun- 
cotton 40 per cent, acted on by acetone, with certain other 
substances added. 

The mixture is incorporated in a small wheel-mill, cov- 
ered to prevent loss of solvent. After incorporation the 


plastic mass is pressed by hydraulic pressure through a hole, 
in the centre of which is a rod. This forms the mass into a 
hollow cylinder or pipe. As the cylinder passes out of the 
hole, it is cut open longitudinally by a cutter, and is spread 
out into a flat sheet, about 10 inches wide and -J inch thick. 
This sheet is run through a set of rollers with transverse: 
grooves and ridges. By this means the sheets are cut into 
a series of strips, but the strips are not entirely separated, as 
they are still united by a thin film of the material, so that 
the sheet can be handled as a whole. These sheets are then 
passed under a cutter, acting at right angles to the strips, 
by which they are cut into grains. The length and width 
of the grains are about equal. By this operation most of 
the grains will be separated from each other. Those that 
stick are rubbed on a sieve or rolled in a barrel. The 
grains are then dried at a temperature of about 51 °.6 C, to. 
drive off the solvent, which is collected, and are finally 
polished and glazed. The size of the grain increases with 
the calibre, ol the gun, and must be determined by experi- 
ment for any particular gun. 

The above particulars were furnished by Mr. W. R. 
Quinan of the California Powder Company. 

This powder is also being tried by the United States, a 
lot of 5000 lbs. having been purchased for the caL-30 rifle. 

Mr. Longridge gives the following as the relative energies 
in foot-tons developed by equal weights of the three powders 
given below, the energy of brown powder being unity: 

Cordite 4.16 

Ballistite 3.44 

Poudre B. N 2.48 

67. Conditions to be Fulfilled by Smokeless Powders — Smokeless- 
ness — Velocities and Pressures — Stability. 
Conditions. — Smokeless powders should fulfil the fol- 
lowing conditions : 

1. They should be approximately smokeless. 

2. They must give high and uniform velocities, with safe 
and regular pressures. 

3. They must be chemically and physically stable, under 
varying conditions of moisture, temperature, and age.. 


4. They must not cause excessive fouling, or excessive 
heating of the gun. 

5. They must not be sensitive to friction or shock. 

6. The manufacture should not be difficult or danger- 
ous, or the ingredients very expensive. 

7. The products of combustion should not be noxious, 
and should not corrode the gun. 

8. There must be no chemical action upon the cartridge- 

9. They should give the required ballistic results with 
reduced weight of charge, and the charge should not 
occupy a large volume, and should be so grained as to be 
loaded in the ordinary loading-machine. 

Smokelessness. — Nearly all the powders introduced 
satisfy this condition. Those of class 3, however, are the only 
ones which are in general truly smokeless, but the smoke from 
the others is rapidly dissipated. In most of them a slight 
mist is visible, since the water formed in the explosion is 
condensed by the air, and the priming or lubricant or the 
slowing agent also produces visible smoke. 

Velocities and Pressures. — Very few of the powders 
fulfil this condition. 

Experiment shows that, especially for small arms, a very 
slight variation of size of grain, weight of charge, or density 
of loading gives a great variation of pressure. For instance, 
a variation of weight of one grain in the small-calibre rifle 
increased the pressure from 44,740 to 51,620 lbs. per square 
inch, while the velocity was increased only 88 ft.-secs. 

Chemical and Physical Stability. — This is another 
point about which there is great doubt. Most of these 
powders are of such recent date that sufficient time has not 
elapsed to test their stability. They are generally made as 
wanted for purposes of experiment, and used in a short time. 
Tests are being made, however, upon this subject by all 

Cordite has been tested as to changes of climate in India 
and Canada with good results. ' 

Ballistite has been soaked in water, dried and fired, with 
very little change in ballistic qualities. 


■88. Fouling — Sensitiveness — Safety and Cost of Manufacture — ■ 
Character of Products of Explosion — Chemical Action — 
Weight of Charge and Specific Gravity. 

Fouling. — As a rule there is very little fouling with 
smokeless powders. The fact that they are smokeless in- 
dicates at once the absence of the residue of solid particles 
which causes fouling with ordinary black powders. This 
absence of fouling, however, has proved to be a disadvantage 
in small arms, owing to the increased friction between the 
bullet and the bore, which the fouling prevented, by acting 
as a lubricant. This friction has sometimes been so great as 
to strip the covering off the bullet and leave it in the bore. 

Various lubricants have been tried to overcome this 
defect, but none of them have proved satisfactory, and the 
defect has been overcome by using a proper covering for 
the bullet, either of copper, nickled steel, or German silver. 

Sensitiveness. — All the powders are safe in this respect, 
and have been pretty thoroughly tested. The difficulty lies 
in the opposite direction, as they are so insensitive that they 
are difficult to explode, and for most of them, special primers, 
or more powerful ori6s, are required. 

Nitro-cellulose powders are specially insensitive. 

Safety and Cost of Manufacture. — The principal 
danger arises in the manufacture of the ingredients, nitro-gly- 
cerine and gun-cotton, and in handling the former. While 
explosions sometimes occur, the manufacture can hardly be 
considered more dangerous than that of gunpowder. The 
question of cost is subordinate to that of efficiency, and 
would only enter in deciding between two or more powders 
of equally good ballistic properties. 

Character of Products. — The character of the gaseous 
products differs very little from those of gunpowder, being 
principally CO, CO a , H a O, and N, and hence no danger is to 
be apprehended from them, and they should not corrode the 
gun. Corrosive effects have been noticed, but they are due 
to the great heat of the gases. 

Chemical Action. — So far as is known, these powders 
do not act chemically upon the cartridge-cases. 

Weight of Charge and Specific Gravity. — These 


powders have much higher ballistic qualities than the old 
nitrate powders, and hence a much smaller charge will give 
greater velocities. The weight of the charge, for the .30- 
cal. rifle is 37 grains, and that of the projectile 220 grains. 
That of the old caL-45 rifle was, powder 70 grains, bullet 
500 grains. 

This reduction in weight of cartridge has an important 
bearing upon the number of rounds carried by the soldier. 
It is evident that with a magazine arm the number of car- 
tridges used will be greatly increased, and the reduction 
in weight enables them to be carried with ease. 

The specific gravity and gravimetric density of the new 
powders are less than those of the old, and hence they oc- 
cupy a greater volume for the same weight; but as the 
weight necessary to give the same or better results is less 
for each charge, the decrease in density occasions no diffi- 

69. Cause of Ballistic Superiority of Smokeless Powders. 

The superior effects of the smokeless powders may be 
explained by considering their potential, force, and rapidity 
of reaction. 

1. Potential. — This is much greater than with the old ni- 
trate powders, as the quantity of heat evolved in the com- 
bustion of gun-cotton and nitro-glycerine is very much 
greater than that of ordinary powder. This heat measures 
the quantity of work which the gases can do upon the pro- 
jectile, and hence the energy of the latter is much greater, 
and we have higher velocities. 

2. Force. — This is also greater than with the old powders, 
as the specific volume of the gases and their temperature 
are higher. 

The specific volume is greater because all the powder is 
converted into gas. This force tends to increase the press- 
ure exerted by the gases upon the gun at the origin, and 
hence this pressure would be very great if it were not 

, 3. The Rapidity of Reaction is very much decreased, so 
that the gas is given off slowly, and allows the projectile 


to start from its original position before this pressure has 
reached too great a value. 

These powders burn very slowly in air, but, like the ni- 
trate powders, their rate of burning increases very rapidly 
with the pressure, and probably if this pressure were very 
high they would detonate. 

Another circumstance concurs to prevent this, however, 
and that is that the powder has no solid residue, and hence 
all the space in the powder-chamber and in rear of the pro- 
jectile is occupied by the gas. In ordinary powders about 
.57 of this space, or more than half, is occupied by solid 
residue. Hence the pressure is kept down at first, and, 
owing to the high temperature and great volume of the gas, 
it is maintained better along the bore than with the old 

We have therefore in the new powders a propelling 
agent which for less weight gives safe pressure at first, 
more gas, more heat, and more sustained pressure than the 
old powders, and hence their ballistic superiority. 


(From Cundill's " Dictionary of Explosives.") 

I. Nitrate Mixtures. 

Name. Composition. 

Nitre, 101 parts 

Amide Powder \ Ammonium nitrate, 80 " 

Charcoal, 40 " 

II. Chlorate Mixtures. 

1 part 

Rack-a-rock \ Chlorate potash, 3 parts 

( Mono-nitro-benzine, 

III. Nitro Compounds. 

.,,.„,.,. ( Gun-cotton 

Abels Glyoxihne \ . T .. , 

' ( Nitro-glycerine 

! Gun-cotton 
Potassium nitrate 



.<Etna Powder. 

Atlas Powder (A) . 

Bellite . 

Nitro-glycerine, 15 to 65 parts 
Sodium nitrate 

' Sodium nitrate, 2 parts 

Wood fibre, 21 

Magnesium carbonate, 2 
Nitro-glycerine 75 

Ammonium nitrate 83 
Tri-nitro-benzine 17 

Blasting Gelatine Di-nitro-cellulose dissolved in nitro- 


Borland Powder \ ( Nitro-glycerine, 


Dittmar Powder 

90 parts 











Potassium nitrate 

Dynamite No. 1 \ Nitro-glycerine, 

( Kieselguhr, 

Giant Powder (See Dynamite.) 

Judson Powder Gunpowder coated with nitro-glyceriner 

Lithofracteur (See Rendrock.) 

C Sugar of manna 
Nitro-mannite J Nitric acid 

( Sulphuric acid 

r Potassium nitrate, 40 parts 

Rendrock J Nitro-glycerine, 40 " 

I Wood-fibre, 13 " 

L Paraffine, 7 " 

( Ammonium nitrate 

( Chlorinated di-nitro-benzine 

' Nitro-lignin 
Potassium nitrate 
Barium nitrate 

I Sawdust 

I Paraffine 

( Gun-cotton 

\ Barium nitrate 

Roburite . 

Shultze Powder 

(a sporting powder) 



IV. Picric Powders. 

■d , „ , ( Ammonium picrate, 

Brugere s Powder -J . " ' 

( Potassium nitrate, 

54 parts 
46 " 



Potassium picrate, 9 parts. 

Designolle's Powder \ Potassium nitrate, 80 " 

Charcoal, 11 " 

1 Gun-cotton dissolved in ether 

Melinite I Picric acid 

( Cresylic acid 


V. Sprengel Mixtures. 

j Di-nitro-benzine 
I Nitric acid 
Rack-a-rock (See ante.) 

VI. Miscellaneous. 

( Chlorate potash 
{ Amorphous phosphorus 
' Fulminate mercury, 6 parts 

Potassium chlorate, 6 " 

Antimony sulphide, 4 " 
Ground glass, 2 " 

) ( Mercury 

Mercury ( ) Nitric acid 

Fulminate J J Akohol 

r Tin cases filled with powder and hav- 

Railroad Fog-signals. •] ing cones with ordinary percus- 

( sion-caps. 

Caps for Toy Pistols . 





70. Definition of Gun-steel — Chemical Composition — Different Con- 
stituents and their Effect. 

Definition. — Steel is an alloy of iron and carbon, the 
percentage of the latter being from to 2.5. This per- 
centage, however, does not always serve to classify steel, as 
it runs into wrought iron on the one hand, and into cast-iron 
on the other. It is distinguished from cast iron by its 
quality of becoming hard when heated to a certain tem- 
perature and cooled quickly, and of having this hardness 
reduced by a process called tempering. 

It is distinguished from wrought iron by this same qual- 
ity, and also by being cast into molds or ingots, which is not 
possible with wrought iron, the latter not being fluid except 
at very high temperatures. In gun-steel the proportion of 
carbon is low, not exceeding 0.5 per cent as a rule. 

Chemical Composition. — Upon this point there is great 
difference of opinion. Steel is called an alloy of iron and 
carbon, but the exact condition of the carbon is not known. 

It is sometimes called dissolved carbon for the harder 
steels, and undissolved for the softer ; also " hardening " 
and " cement " carbon, for the harder and softer steels re- 
spectively. More recently it is called " fixed " carbon for 
the hard, and "free" carbon for the soft steels. These two 
carbons may be changed from the one to the other, as the 
result of special treatment. 

Other Constituents. — Besides the carbon, there are 
always other substances present, some of which are bene- 


GUNS. 137 

ficial and others injurious to its quality. Among the prin- 
cipal of these substances are : 

1. Sulphur. — This is injurious to the steel, as it makes it 
■difficult to forge, producing " hot-shortness," or brittleness 
when hot. 

2. Phosphorus. — This is also injurious, as it has the effect 
of making steel brittle when cold, or " cold-short." 

3. Manganese. — This when added in proper proportions 
improves the quality of the steel, rendering it hard and 

4. Silicon. — Is valuable, as it forms a fusible slag with the 
iron oxide in manufacture, and prevents the formation of 
gas, and consequently of blow holes in the steel. If in too 
great quantity, it causes brittleness. 

5. Chromium.— Gives great hardness to steel without 
brittleness, and hence the best forged steel projectiles are 
made of chrome-steel. 

6. Nickel. — This gives great toughness to steel, so that 
armor-plates made of nickel-steel resist racking very well. 

Nickel-steel is also being experimented with for guns, at 

71. Physical Qualities — Hardness — Toughness — Elastic Limit — 
Hooke's Law — Tensile Strength. 

Hardness. — Gun-steel should be sufficiently hard to re- 
sist deformation from blows, and also the action of the pro- 
jectile and the powder-gases; but hardness is generally 
-accompanied by an undesirable quality, brittleness, and 
hence a modification called toughness is sought in this metal. 

Toughness is the quality which enables a metal to under- 
go considerable change of form under the action of a force, 
without rupture, and with great resistance to that change. 

Elasticity and Elastic Limit. — When a tensile stress 
or force is applied to a piece of steel, it will elongate a cer- 
tain amount. 

This total elongation, divided by the original length, will 
give the elongation per unit of length. When the stress or 
force ceases to act, the steel will recover its original length, 
provided the stress is not too great. If an additional force 


be applied, a similar effect will be obtained, the elongation 
per unit of length being greater in this ease, and the metal 
returning again to its original length when the stress ceases 
to act. The same effects will be observed till the stress 
reaches a certain amount, when the metal will not return to 
its original length, but will acquire a permanent set. If the 
stress next below the one which produces the permanent set 
be measured, and be divided by the area of cross-section of 
the metal, it will give the elastic limit of the metal ; and if the 
elastic limit be divided by the corresponding elongation per 
unit of length, the result will be the modulus or coefficient 
of elasticit}' of the metal. 

Let a be the area of cross-section of the metal ; 

/, its length ; 

K, the total elongation ; 

W, the stress acting at the elastic limit ; 

E, the modulus of elasticity ; 

0, the elastic limit. 



« = — ; 


K ~ aK' 

Denoting by A. the elongation per unit length, we have 

* = £. 



Hooke's Law. — The ratio of stress to elongation remains 
constant up to the elastic limit, and this constant ratio is the 
modulus of elasticity E. This is expressed as follows : 

GUNS. 139 

Within the elastic limit of a metal, the stress is propor- 
tional to the strain. This is called Hooke's law. 

If we compare two kind's of steel, one having a high per- 
centage ot carbon, and the other a low percentage, it will 
be found that the steel high in carbon has a high elastic 
limit, and that low in carbon a low limit. Since the modulus 
of elasticity for all steel is nearly constant, and equal to 
about ' 30,000,000 lbs. per square inch, the high steel wilL 
elongate more at the elastic limit than the low (equation 
169)). From this alone it would appear that the high steel 
is best for gun-construction, since it enables the metal to 
yield more to the stresses of the powder-gas, and to recover 
its original form without permanent set. 

The reason why high or hard steel is not used is, that it 
is liable to flaws, strains, or incipient cracks, produced in 
manufacture, especially in large pieces. A hard steel is 
also dangerous, because after passing its elastic limit, it has 
very little remaining strength, and breaks easily, and with 
little warning, while the soft steel yields considerably with- 
out fracture, after passing the elastic limit, exhibiting the 
quality of toughness, previously defined. 

Tensile Strength. — By this is commonly understood 
the stress per unit area required to rupture the metal. It is 
not of great importance ih gun-steel, although limits are 
prescribed for it in the tests, since we consider the elastic 
limit only in gun-construction. 

For clearness, a tensile stress only has been considered. 

The same relations hold, however, for compression or 
torsional stress, and each has its corresponding elastic limit, 
and modulus. 

72. Structure of Steel — Defects — Blow-holes — Pipes. 

Structure.— Steel is always a crystalline metal, and has. 
no fibrous structure like wrought iron. These crystals are 
generally small, and vary in size and appearance with the 
treatment the metal receives after casting. They are very 
small in the best steels, and may be so small that the frac- 
ture will lose its crystalline appearance. 


Defects. — These are common to all cast metals, and 
^teel has some in addition peculiar to itself. 

Slow Cooling in large masses gives large crystals, and 
consequently a weak steel. It also causes a lack of uni- 
formity in the steel. This being an alloy of iron and car- 
bon, and the carbon being combined in different proportions 
throughout the fluid mass, the alloys highest in carbon are 
the lightest, and will rise to the top. Hence the hardest 
steel is found here. For the same reason, the softest will 
be at the bottom of the ingot. The middle portion of the 
length will therefore give the best steel. As the fusibility 
of the steel increases with the percentage of carbon, those 
portions low in carbon will solidify first, and hence, in the 
same cross-section, the part high in carbon will be near the 
centre, where the mass remains fluid longer. 

Blow-holes. — This defect is peculiar to steel, and is due 
to the gases in the melted metal, which, being unable to es- 
cape, are imprisoned in the casting, and form holes. These 
blow-holes are causes of weakness in steel, as it is impossible 
to discover them, and forging or compression only changes 
their form, but does not remove them. Various theories 
have been advanced to account for their presence, and at- 
tempts made to get rid of them. They are more prevalent 
in the Bessemer than in the open-hearth steels, by which 
latter process gun-steel is made. 

The lower the temperature at which the steel is cast, the 
"more apt are these blow-holes to occur, because the metal 
hardens before the gas has time to escape. 

Pipes. — These are cavities formed in the axis of the 
ingot, due to internal strains from cooling. They generally 
occur when the metal is cast too hot. Thus on the one 
hand too low a temperature causes blow-holes, and too high 
a temperature pipes. 

To avoid these defects in gun-steel, 6 per cent of the 
total weight of the cast ingot is cut from the bottom 'and 
33^ per cent from the top, the remainder being used for the 
lorging. The piping and weak metal in the centre of the 
ingot are removed by boring or cutting out the central part 
of the ingot Blow-holes can be prevented only by careful 

GUNS. 141 

treatment in casting, and their presence cannot be detected 
except by subsequent working, and not then if they are. 
beyond the reach of the tools employed. 

73. Working dualities of Steel — Fusibility — Malleability and 
Ducti lity — Welding — Annealing. 

Fusibility. — This quality enables steel to be cast into 
various shapes, and into ingots for gun-forgings. It re- 
quires, however, a relatively high temperature, and has 
caused the introduction of various special processes for 
obtaining this temperature. In the Bessemer process, the 
heat necessary is obtained, by blowing air through a melted 
mass of cast iron, by which the carbon and silicon are oxi- 
dized, and a high temperature produced. In the open- 
hearth process, the high temperature is obtained by the use 
of gaseous fuel, and by storing up the waste heat of the fur- 
nace in chambers of fire-brick, through which the gaseous 
fuel passes, and by which it is raised to a high temperature. 

Malleability and Ductility. — Steel, when heated to 
a red heat, possesses the property of malleability, and it is 
due to this fact that it can be forged into any shape. When 
cold, owing to its ductility, it can be drawn into wire, which 
is used in wire guns and for various other purposes. 

WeldiNG. — Ordinarily steel cannot be welded except 
when very low in carbon, and approaching wrought iron. 
Lately, however, the process of electric welding has been 
introduced, and by it the welding can be readily accom- 

Annealing.. — -This is a very valuable property possessed 
by steel. By heating it to a certain temperature and allow- 
ing it to cool slowly, a piece of hard steel will become soft, 
so that it can be readily worked in the lathe. After work- 
ing, it can be returned to its former hard condition, by 
heating it again, and cooling it quickly. After forging or 
working steel, it generally has internal strains due to these 
processes, and these strains may be removed by annealing. 
By cooling in oil, the tensile strength and elastic limit of 
steel are greatly increased, and these qualities, especially 
elasticity, are very valuable in gun-construction. 



74. Manufacture of Gun-steel— Open-hearth Process — Gas-producer 
and Regenerators. 

Open-hearth Process. — All gun-steel at the present 
day is made by this process, which derives its name from the 
fact that the receptacle in which the steel is melted is open 
at the top, and exposed to the flame of the fuel which plays 
over the surface, and performs a principal part in the forma- 
tion of the steel. It is also called Siemens or Siemens-Martin 
steel, according to the ingredients used to form the steel. 

Apparatus. — The furnace used^is that invented by Dr. 
Siemens, and a general description of it is given. It con- 
consists of the following essential parts : 

1 . The gas-producer ; 

2. The regenerators; 

3. The furnace proper. 

The Gas-producer. — The fuel used in the Siemens fur- 
nace is gaseous, and is obtained from ordinary fuel, by sub- 
jecting the latter to a preliminary process in the gas-produ- 
cer. This apparatus, Fig. 29, consists of a rectangular 

Fig. 29. 

chamber of fire-brick, one side, B, being inclined at an angle, 
ot 45 to 6o°. A is the grate. The fuel, which may be of 
any kind, is fed into the producer through the hopper C. 
As the fuel slowly burns, the CO, rises through the mass 
above it, and absorbs an additional portion of C, becoming 
converted into 2CO. This gas passes out of the opening D, 
into a flue. In order to cause it to flow towards the furnace, 
it is led through a long pipe, E, where it is partially cooled, 



and it then descends the pipe F leading to the furnace. The 
gas in F being cooler than that in E and D, a constant flow 
of gas from producer to furnace is maintained. 

The Regenerators. — The gas entering the furnace is, as 
has been stated, CO. To burn it to C0 2 , air must be mixed 
with it. This mixture is made in the furnace proper, the 
CO and air being kept separate till they reach the point 
where they are to burn. The CO is cooled to some extent, 
as shown, before being admitted to the furnace. 

To heat both air and CO before they are mixed and 
burned, and to accomplish this economically, and raise them 
to a high temperature, the waste heat of the furnace is em- 
ployed. This is the object of the regenerators, Fig. 30. 

Fig. 30. 

They consist of four large chambers below the furnace, 
tilled with fire-brick, piled so that there are intervals be- 
tween the bricks to allow the gas and air to pass through. 
Their action is as follows : When the furnace is started, 
CO is admitted through A and air through B, both A and 
B being cold. These pass up through the fire-bricks in A 
and B and through flues at the top, and flow into the fur- 
nace proper, where they are lighted. The products of 
combustion are caused to pass through C and D, which are 
similar chambers. In doing so these products heat the fire- 
bricks in Cand D. After some time, — about one hour gen- 
erally, — by the action of valves controlled by the workmen, 
the CO and air are caused to enter the furnace through C 



and D respectively, and the products of combustion to pass 
out through A and B. In this case the CO and air entering; 
the heated chambers C and D are raised to a high tempera- 
ture before ignition, and the temperature of the furnace 
thereby greatly increased. It is also evident that A and B 
will be more highly heated than C and D were, and hence 
when the next change is made the gas and air passing 
through A and B will be more highly heated than when 
passing through C and D, and so on. 

The action of the furnace is therefore cumulative, and 
its only limit in temperature is the refractoriness of the 
material. By regulating the proportions of gas and air, 
which is readily done, the temperature may be kept con- 

75. Manufacture of Steel — The Furnace — Operation — Crucible 
The Furnace. — The furnace proper consists (see Fig. 
31) of a dish-shaped vessel D of cast iron, supported so that 

Fig. 31. 

the air can circulate freely around it and keep it from melt- 
ing. This is lined with refractory sand S\ and in order to 
repair it when necessary, the pan D is generally arranged so 
that it can be run out of the furnace. This allows it to cool 
quickly. The pan is placed over the regenerators, and the 
gaseous fuel and air enter by the flues F, and the products 
of combustion escape by the flues F', or the reverse, ac- 
cording to the position of the regulating-valves. 

The arrows show the direction of these currents. The. 

GUNS. 145 

roof R is lined with fire-brick, and by its shape deflects the 
flame over the metal in the hearth. At opposite ends of 
the furnace are a charging-door for admission of the metal, 
and a tap-hole for drawing off the finished steel. These are 
not shown in the drawing. 

Operation. — The principle of the process is that when 
wrought-iron or steel scrap is added to melted cast iron, the 
percentage of carbon is thereby reduced till it reaches that 
required for steel. The charge consists of pig-iron heated 
red-hot in a separate furnace, and then placed on the hearth 
of the Siemens furnace. By the action of the furnace this 
pig-iron is soon melted. Scrap wrought iron or steel is them 
added in suitable proportions, till the percentage of carbon 
is low. When it has reached the proper point, the percent- 
age! is made exact by adding a pig iron containing a known 
percentage of carbon, such as Spiegeleisen or ferro-manga- 
nese, or by the addition of ore. The percentage of carbon 
is judged of during the process by taking samples from 
the melted metal, cooling them, observing their fracture 
on breaking, and by dissolving portions of the specimen in 
HNO, and comparing the color with that of standard solu- 
tions of steel in HN0 3 containing different percentages of 
carbon. In this way the composition of the steel can be 
exactly regulated, as the metal can be kept in a melted 
state without damage for a considerable time, and the char- 
acter of the flame made oxidizing or reducing at will, ac- 
cording to the relative amounts of air and CO admitted. 

The operation ordinarily lasts about eight hours for 
each charge. 

When the steel has attained its proper composition, the 
furnace is tapped and the metal cast into ingots, ready for 
the succeeding operations. 

Crucible Process. — This is used by Krupp. The in- 
gredients of the steel are melted in crucibles, and the result- 
ing steel from the crucibles is poured into a common reser- 
voir from which the ingots are cast. 

The Bessemer process, though important and producing 
large quantities of steel, is not as yet used in making gun- 



Fig. 32. 

76. Casting Ingots — Ladle — Crane — Ingot-mold— Pouring — Sink- 
ing Head. 

After the proper percentage of carbon is obtained, the 
steel is cast in ingots. 

Ladle. — The first step is to tap the furnace and draw 
off the steel into a ladle. This ladle is made of boiler-iron 
lined with refractory sand. It has two trunnions on the 
exterior which support it, and around which it revolves 

when tipped, to pour the metal into 
the mold ; or it may have a tap- 
hole at the bottom closed with a 
plug of fire-clay, which is lifted by 
an iron rod covered with refractory 

In Fig. 32, T is the tap-hole, T 
the trunnions, R the rod, and S its 
casing. The advantage of tipping 
is that it is quicker, and of the tap- 
hole, that it gets rid of scoria and impurities on the surface 
of the melted steel, and keeps them out of the mold. 

Crane. — This is used to convey the ladle to the molds, 
or, more generally, for handling the ingots and molds 
after the casting. It is very ^ ^ 

often found more convenient 
to run the ingot-molds on 
cars under the ladle, or under a 
spout attached to the furnace. 
Ingot-molds. — These are 
generally made of cast iron, 
and are circular in cross-sec- 
tion, to insure uniform cooling. 
They are in one piece, and 
slightly conical on the inte- 
rior, so that the ingot, after 
casting, may be readily with- 
drawn. They may also be 
made in halves, parting on solid. 

an axial plane ; but in this 


Fig. 33. 

case they are liable to open at the joint, due to warping. 

GU/VS. 147 

The interior surface is protected by a wash of clay or 
plumbago. Melted steel poured into an ingot-mold will 
not adhere to the sides, while melted cast iron will adhere. 
The reason is that the steel chills and contracts away 
from the mold, while the iron cools more slowly and fuses 
the mold. The general shape of the ingot-molds is shown 
in Fig. 33. 

POURING. — If the steel is very hot, it must be poured 
slowly into the molds in a thin stream. This allows the 
gases time to escape. If at a lower temperature, it may be 
poured more quickly. 

The ingot-molds may be warmed before casting to pre- 
vent undue cooling and consequent strains, and also the 
formation of pipes. 

After the steel is cast, the molds must be covered to ex- 
clude air and cause slow cooling. 

Sinking-head. — In all castings, whether of iron, steel, or 
other metal, an excess of metal, called the sinking-head, is 
left at the top of the mold. This column of metal acts by 
its weight to give greater density to the lower portions of 
the ingot ; it also serves to collect the scoria and impurities 
which rise to the top, and it fills any cracks or cavities that 
may form in the cooling of the ingot. It is necessary to 
keep this sinking-head fluid as long as possible, and hence 
it is generally cast in a sand-mold lor gun-ingots. 

77. Whitworth's Process of Fluid Compression. 

This process was invented by Sir Joseph Whitworth of 
England, and gives by hydraulic pressure, the same effect 
as that due to the sinking-head. It may be regarded as an 
artificial sinking-head of great height. The process con- 
sists in forcing the piston of a hydraulic ram down upon 
the melted steel in the mold, and maintaining the pressure 
till the steel solidifies. The ingot-mold used in this process 
must be very strong to withstand the great pressure, and it 
has a peculiar arrangement by which the gases driven out 
by the pressure are allowed to escape. Fig. 34 gives the 
general arrangement. 

The mold consists of a strong cast-steel cylinder, A, 



with its bottom, B. This cylinder is lined with rectangular 
bars of wrought iron, C, which have 
grooves, D, cut at intervals along their 
faces in a radial direction. Their rear 
edges are also cut off longitudinally so 
that when placed side by side and forming 
a lining for the cylinder A they have con- 
tinuous longitudinal channels, E, parallel 
to the elements of the cylinder. The 
grooves D communicate with the channels 
E, and thus allow the gas to escape at the 
top and bottom of the mold. The interior 
of the mold is lined with refractory sand. 
Action. — When the melted steel is 
poured into the mold and the ram R 
forced down upon it, the hot metal is at 
first forced through the openings O be- 
tween ram and mold. But the metal 
quickly cools and forms a solid mass,, 
completely closing these openings O. The 
gas is forced out through the channels as shown, and 
the effect of the pressure and shrinkage is to shorten the 
ingot about i£ inches for each foot of length. 

Theory. — It appears at first that the metal, as well as the 
gases, would be expelled through the channels, and also 
that, since fluid pressure is equal in all directions, there is no 
reason why this pressure should force the gas out of the 
melted metal. Dr. Siemens suggests as an explanation that 
the steel cools first on the exterior where it is in contact 
with the mold, and offers a greater resistance here to the 
motion of the ram. It is broken up in consequence by the 
pressure, and becomes porous. The interior of the mold - 
remaining fluid, and offering less resistance than the outside, 
receives consequently more compression, and hence the re- 
sult will be to force the gas outward through the porous 
exterior. This porous exterior, while allowing the gas to 
escape, retains the fluid metal. It is also claimed that the 
pressure increases the solvent action of the metal upon the 
gases. Krupp maintains, however, that this process of 



fluid compression simply closes up the cavities but does not 
■expel the gas. 

78. Treatment after Casting — Testing — Reheating — Forging — 
Cranes — Hammer. 

Testing. — After the ingot is cast and cooled, specimens 
of it are tested chemically to determine its composition, 
and also in the testing-machine to determine its physical 
qualities. The ingot is graded according to these tests, 
and a hole is then bored through it parallel to its axis, re- 
moving the central part of the ingot. This hole is for 
purposes of forging, as will be explained. 

If the ingot is short, this hole may be punched ; and for 
small tubes or any solid forgings the hole is not necessary. 

Reheating. — For forging, the ingot is then reheated in 
a furnace which is a modification of the Siemens. In the 
reheating, care must be taken to apply the heat slowly and 
regularly, so as to avoid overheating the exterior before 
the interior is brought to the proper temperature. If the 
heat is applied too quickly, the ingot is liable to crack from 
unequal expansion, and the exterior to be overheated or 
" burned." 

Cranes. — The ingots when heated to the proper temper- 

Fig. 35. 

ature are handled by heavy cranes, which remove them from 
the furnace and carry them to the hammer or press. They 


are slung from the crane by a chain called the sling-chain„ 
and are balanced by the addition of extra weights at the 
cool end, so that they may be readily swung by the work- 
men, and turned axially under the hammer. Fig. 35 shows 
the general arrangement for forging an ingot under a ham- 
mer. H is the hammer, A the anvil, C the crane, E the in- 
got, S the sling-chain, P the porter-bar; the handles K are 
used for rotating the ingot under the hammer. 

Hammer. — The steam-hammer is used in forging ingots, 
except where hydraulic pressure is preferred. These ham- 
mers consist of a heavy head or tup attached to the piston 
of a steam-cylinder. The cylinder is vertical and is sup- 
ported by two legs, and the hammer thus formed is .called 
an A hammer, from its general appearance. When the 
steam raises the hammer, and is then exhausted, and the tup 
allowed to fall by its own weight, we have a single-acting 
hammer ; when the steam acts also to drive the tup down,, 
we have a double-acting hammer. The foundation for the 
anvil is separate from the hammer to diminish the effect of 
the blow upon the latter. 

Since the same energy may be obtained from a light 
hammer moving quickly or from a heavy hammer moving 
slowly, the latter is preferred for heavy masses, as the effect 
of the blow is better distributed through the mass. Armor- 
plates are generally made by hammering, as the effect of 
the blow is felt more on the face and less in the interior, and 
it is important to have a good qualify of face. With gun- 
forgings both hammer and hydraulic pressure are used 
with excellent results, the hydraulic press, however, being 
preferred, as it is more slow in its action and distributes, 
the effect throughout the mass. 

79. Whitworth's Hydraulic Forging — The Press — Mandrels. 

In this process the ingot is drawn into shape by the 
pressure of a powerful hydraulic ram. As the action is slow, 
it is claimed that the effect is better distributed throughout 
the mass, as before stated, and consequently produces a 
better effect upon the metal as a whole. 

The Press. — This is a large hydraulic ram so arranged- 



that it may be quickly adjusted to any size of ingot. The 
general arrangement is represented in Figs. 36 and 37, 
although the ram actually has many arrangements for ad- 
justment, etc., not shown. 

The Mandrels. — With this press a secondary or mov- 
able anvil, called a mandrel, is used. It is shown in Figs. 36 
and 37, and its use is as follows : 

If the ingot is to be drawn out into a long forging such 
as a gun-tube, it is first bored out on the interior. It is 
then heated, and the mandrel passed through the bore. The 
ingot is now placed under the forging-press, resting on the 
fixed anvil as shown in Fig. 36. When pressure is applied 








Fig. 36. 

under these circumstances, the effect will be to lengthen the 
ingot, keeping its interior diameter unchanged. On the 
other hand, if the ingot is to be forged into a hoop, it is 
bored as before, heated, and the mandrel passed through 
the bore; but in this case the ends of the mandrel are sup- 
ported as shown in Fig. 37, the ingot being allowed to swing 
on the mandrel. 

When the pressure is applied under these conditions, it 
is evident that the walls of the ingot will be compressed, 
the interior diameter increased, and the length of the ingot 
will remain practically unchanged. 

In the first case we have a fixed mandrei, and in the 
Second a swinging mandrel. A current of water sometimes 



circulates through the centre of the mandrels to keep them 
cool, and in the case of the fixed mandrel, it is .withdrawn 
from the forging by a second hydraulic press acting on it. 

Comparing the hammer and press, it is claimed for the 
hammer that its effects are more local, and therefore that it 





=. ■*= 







Fig. 37. 

is better for armor-plates ; that the effect of its blows is to 
heat the metal, and therefore the temperature may be lower 
in forging ; and that it uncovers defects in the metal, while 
the press conceals them. 

80. Gun-forgings— Treatment after Forging — Annealing — Boring 
and Turning — Oil-tempering — Re-annealing — Tests. 

Gun Forgings.— The principal gun-forgings are the 
tube, the jacket, and the hoops. 

The forging of the tube and hoops has been explained, 
and that of the jacket is exactly similar. 

Annealing. — After forging, the hammer or press leaves 
certain strains in the metal, and they must be removed. 
This is done by annealing. This process consists in heating 
the -forging carefully to a certain temperature, which is de- 
termined by experience, and allowing it to cool slowly, in 
the furnace, the latter being allowed to cool naturally. 
By this process the steel becomes soft, and all strains are 

Boring and Turning.— The forging is now placed in a 

GUNS. 153 

iathe and bored and turned to near its finished size. Pieces 
are also taken off the ends as specimens, and tested, to de- 
termine the qualities of the metal and as a guide to subse- 
quent treatment. 

Oil-tempering. — The object of this process, to which 
the forging is now subjected, is to give the peculiar prop- 
erty called " toughness " to steel. The practical effect is 
that it increases the elastic limit and tensile strength, and 
reduces the elongation before rupture. 

Process. — The forging is slowly heated and carefully 
inspected, till all the parts have acquired the same tem- 
perature, which is judged by the color. A long forging is 
generally heated vertically to avoid warping. When at 
the proper temperature, it is raised by a crane and lowered 
vertically into a tank of oil, a current of which is caused to 
flow through the bore. The oil is surrounded by a water- 
jacket to keep down the temperature. 

Being a poor conductor of heat, the oil allows the steel 
to cool correspondingly slowly, and' thus gives the particles 
time to adjust themselves, and the result is a considerable 
increase in elasticity and tenacity, and it acquires the prop- 
erty of toughness already defined. 

Re-annealing. — The process of oil-tempering causes 
internal strains in the metal, and these are removed by 
reannealing as before. This annealing process reduces 
slightly the elastic limit and tensile strength and increases 
the elongation before rupture. 

Tests. — The physical qualities of the metal are now 
tested. For this purpose specimens are cut from the 
breech and muzzle ends of each tube, jacket, or hoop forg- 
ing, and the results of these tests compared. No great 
difference in quality must exist between breech and muzzle 
specimens, as this would indicate a variation in quality of 
the metal from breech to muzzle. In the U. S. service the 
requirements of the Ordnance Department are about as 
follows : 

Elastic limit, 46,000 to 50,000 pounds per square inch ; 

Tensile strength, 86,000 to 93,000 pounds per square 


Elongation at rupture, 15 to 17 per cent in a length of 3 

81. Brinell's Experiments. 

To determine the effects of heating and cooling on the 
change of structure and the hardening of steel, Mr. J. A. 
Brinell, a Swedish engineer, made a series of experiments. 

Taking a certain kind of steel which contained about the 
same percentage of carbon as gun-steel, he heated bars of 
it to different temperatures and cooled them at different 
rates. After heating and cooling, the bars were broken 
and the fracture carefully examined, and chemical tests 
were made to determine the condition of the carbon. He 
found that there were two states of the carbon — one which 
he called free carbon and which was associated with soft 
steel, and the other, fixed carbon, associated with hard 
steel. In general the soft steel had a crystalline structure 
and the hard steel an amorphous structure, or one in 
which the crystals were so small as to lose their crystalline 

His conclusions were as follows : 

1. For each steel, hard and soft, there is a certain tem- 
perature, called the critical temperature, to which if the 
steel be heated, and be suddenly cooled, all the carbon will 
become fixed, and the structure -will be amorphous. This 
is the hardest condition of steel; and hence, to harden it, it 
is heated to this temperature and cooled suddenly. 

2. Hard steel, if heated to this critical temperature and 
cooled slowly, will acquire the crystalline structure, and all 
the carbon will become free. Soft steel heated to this tem- 
perature and cooled slowly undergoes no change. This is 
the softest condition of steel, and hence, to anneal it, it is 
heated to this critical temperature and cooled slowly. 

3. If hardened steel, or steel which has been subjected 
to the first process, be heated to any temperature below 
the critical temperature, it becomes softer as the tempera- 
ture increases. That is, with hard steel, as the critical tem- 
perature is approached, more and more of the fixed carbon 
becomes free, and if the steel be cooled either slowly or 

GUNS. 155 

quickly after having been heated to any temperature below 
the critical one, the hardness of the steel is diminished. 
This process is called tempering, and by it the degree of 
hardness can be regulated to any extent. It is the process 
commonly employed by the blacksmith in tool-making. 
The less the steel is heated the harder it will be. 

4. When steel is heated to the critical temperature and 
cooled very quickly, as by immersion in mercury or acidu- 
lated water, it becomes harder than if cooled by immersion 
in ordinary water; and on the other hand, if cooled more 
slowly, as in oil, it acquires less hardness but more elas- 


82. General Principles of Machines — Definition — How Motion is 
Transmitted and Modified. 

In order to understand the operations in the manufac- 
ture of a modern gun, some knowledge of the general 
principles of machines is necessary, since all the operations 
upon the gun after the forgings are received, are conducted 
in a machine-shop, and the success of the modern gun as a 
machine for propelling projectiles, depends upon the accu- 
racy with which the machine-work is done in building it. 

Definition. — A machine is any instrument or device 
designed to receive energy from some source, and to over- 
come certain resistances in transferring this energy to other 
bodies. (Michie, p. 246.) 

The mechanical principles of machines are discussed in 
the Mechanics, pages 246-281, and it is intended here to 
give the practical application of these principles as seen in 
the shops. 

Another definition of a machine is, an assemblage of 
moving parts for the purpose of transmitting and modify- 
ing motion and energy. 

How Motion is Transmitted and Modified. — A 
machine receives its motion from some source of energy 
such as the steam-engine, water-wheel, etc., and transmits it 


through a series of wheels, sliding surfaces, etc., to the 
point where the work is done. 

The source of motion is called the driving-point or prime 
mover ; the parts through which the motion is transmitted, 
the train ; and the point where the work is done, the working- 

Motion may be transmitted and modified by : 

1. Rolling contact of two or more surfaces ; 

2. Sliding contact, as in gear-wheels, screws, etc. 

3. Belts or bands ; 

4. Linkwork ; 

5. Cords or ropes ; 

6. Hydraulic connection. 

83. Rolling Contact — Different Forms of Pieces in Rolling Contact. 
Rolling Contact. — Let A and B, Fig. 38, represent two 
wheels whose axes are parallel. When 
motion is communicated to B it will impart 
this motion to A by the friction of the two 
surfaces in contact at the point a. These 
Fig. 38. circles in contact at a are called the pitch- 

circles, or pitch-lines ; the point of contact a, the pitch-point. 
The line cd joining the centres of the wheels is called the 
line of connection, and is the line along which the velocity of 
the moving pieces is zero. 

The general principle which governs the motion of the 
pieces in rolling contact is that each pair of points in the 
pitch-lines which are in contact at any instant, must at that 
instant be moving in the same direction, and with the same 

This principle leads to the following results : 
Since each pair of points in contact must move in the 
same direction at the same instant, the axes of the wheels 
and their points of contact must lie in the same plane, be- 
cause the motion of the points of contact is at right angles 
to the axis of each wheel ; and since the velocities of their 
points of contact must be equal, the angular velocities of 
the wheels must be inversely as their radii. 



Different Forms of Pieces in Rolling Contact.— 
Besides the circular wheels, we may have — 

1. A wheel, A, and rack, B, Fig. 39, 

2. Two wheels with intersecting axes, Fig. 40 ; 

3. Two wheels with axes which are neither parallel nor 
intersecting. This case will not be considered. 

Fig. 40. 

For the wheel and rack, since all points in the wheel move 
at right angles to its axis, while all points of the rack move 
parallel to itself, or at right angles to the axis of the wheel, 
the general principle that the points of contact shall be moving 
in the same direction requires that the axis of the wheel and 
all points of contact must lie in a plane perpendicular to the 
motion of the rack, and that, since the points of contact must 
have the same velocity, the actual velocity of the rack must be 
equal to the product of the angular velocity of the wheel by 
its radius. For the two wheels with intersecting axes, if the 
line ac joining the point of contact a with the intersection of 
the axes be regarded as the line of contact of two cones, 
whose axes are those of the wheels, it is evident that, as the 
surfaces of the cones come into contact along this line, each 
pair of points in contact will be moving at that instant in 
the same direction and with the same velocity. Hence the 
surfaces of two wheels whose axes intersect, are frusta of 
cones, whose element of contact passes through the point of 
intersection of the axes. 

84. Sliding Contact — Principles of Teeth — Figures of Teeth — 
Sliding Contact. — In the method of communicating 
motion by rolling contact, it is evident that no great force 


can be transmitted without danger of the slipping of one 
wheel on the other. If this happens, the velocity ratio of 
the two wheels is not constant, and hence this method will 
not answer for accurate work. Where an exact ratio is to 
be maintained between the velocities transmitted by two 
wheels, these wheels must be so connected that one cannot 
move without the other. 

This connection is usually made by means of projections 
on each wheel called teeth. 

Principles of Teeth. — Their construction and opera- 
tion depend on the following general principles : 

Let A and B, Fig. 41, represent two wheels whose axes 
are a and b, and suppose these wheels 
in contact at c. 

Then the circumferences in con- 
tact are the pitch-circles, as before 
explained. Let 1, 2, 3, etc., represent 
teeth formed upon the wheel A. 
Then the pitch of the teeth is the 
distance de along the pitch-circle 
from the front of one tooth to the front of the next. Hence — 

1. In wheels which rotate continuously for one revolu- 
tion or more, the pitch must be some aliquot part of the 
pitch-circle, in order that it may be contained in that circle 
an even number of times. For a rack, or a wheel which 
does not perform a complete revolution, this condition is 
not necessary. 

2. In order that two wheels, or a wheel and rack, may 
work correctly together, the pitch must be the same in each. 

3. Hence, in a pair of wheels which work together, the 
number of teeth in each wheel is directly as the circumfer- 
ence or radius, and therefore inversely as the number of 
revolutions in a given time. 

Figures of Teeth. — These are regulated by the prin- 
ciple that the velocity ratio given by the teeth sliding on 
each other shall be the same as that given by the pitch- 
circles rolling on each other. 

Action of Teeth.— To give a general idea of this ac- 
tion, let Fig. 42 represent the teeth of two wheels in contact. 





Fig. 42. 

The tooth a of the lower wheel first touches b of the 
upper at the point c. These teeth then slide towards each 
other till the point d is reached, 
when they slide away from each 
other and finally lose contact at e. 
This process continues for all the 
teeth, the arc cd being the arc of 
approach, and de the arc of recess, 
the whole curve cde representing 
the various positions occupied by the point of contact dur- 
ing the action of the teeth. 

The method of describing the figures of teeth is too ex- 
tensive for discussion here. 

85. Belts or Bands — Rounded or Crowning Pulleys — Speed-Cones — 
Starting and Stopping. 

Belts. — When teeth are used to communicate motion, 
they possess the great advantage of preserving always the 
same velocity ratio between two wheels. They have, how- 
ever, the disadvantage of being a rigid connection, so that 
the}' do not allow for starting or stopping, or sudden 
changes of speed. Hence for the transmission of energy 
from the engine or other prime mover to the different ma- 
chines in a shop, belts are almost universally employed. 
After the energy has been received at any machine, the 
parts of that machine are connected by gearing, or teeth, if 
accurate velocity ratios are required. 

Belts are generally made of leather or gutta percha, and 
are broad and flat, and hence require correspondingly shaped 

The velocity ratio of two pulleys connected by a belt 
follows the same principle as in the case of rolling or sliding 


Fig. 43. Fig. 44. 

contact, viz., the actual velocities of all points along the 
belt are the same, and hence the angular velocities of the 



pulleys are inversely as the radii. If the pulleys are to 
move in the same direction, the belt must be open, Fig. 43 ; 
if in opposite directions, the belt must be crossed, Fig. 44. 

Rounded Pulley. — To prevent the belt from leaving 
the pulley, the latter is made crowning or rounded, Fig. 45. 
A belt always moves toward that part 
of the pulley whose radius is greatest, and 
the reason is as follows : When the belt 
moves to one side of the pulley, the side 
ab of the belt becomes compressed, Fig. 
45. The resistance of the side ab to this 
compression produces a force in the direc- 
tion of the arrow e, which straightens the 
belt and causes it to move to the highest 
part of the pulley. 

Speed-cones. — To vary the velocity 
ratio communicated between a pair of par- 
allel pulleys or shafts by a belt, without stopping the mo- 

Fig. 45. 




=dti — u 


Fig. 46. 

Fig. 47. 

tion of the machinery, speed-cones are used, 
be either continuous cones, 
Fig. 46, or stepped cones, Fig. 
47. In the first case we can 
obtain a gradual variation of 
speed, and in the second, cer- 
tain fixed variations only. 

The second method is gen- 
erally used. 

Starting and Stopping. 
— As individual machines require to be started or stopped 
without interfering with the source of power, each machine 
is in general provided with two pulleys. 

These pulleys are mounted on an independent shaft called 
a counter-shaft, and one of them is fixed to this shaft, while 
the other turns freely upon it. When the machine is to be 
stopped, the belt is shifted to the " loose pulley," as it is 
called ; and when started, to the fixed pulley. 

86. Li nkwork— Cords and Ropes— Hydraulic Connection. 

Linkwork. — When two rotating pieces are connected 

guns. 161 

"by a rigid bar, as the driving-wheels of a locomotive, this 
bar is called a link. It may also connect a rotating piece 
and a sliding piece, as the piston-rod and crank of a steam- 
engine, which are connected by a link. In the case of link- 
work, the velocity of all points of the link being the same 
at any instant, the angular velocities of the rotating pieces 
are inversely as the perpendiculars let fall from the axes of 
rotation to the link. 

In the case of a rotating and a sliding piece, as in Fig. 
48, every point of the sliding piece is moving at a given in- 
stant perpendicular to the line ab, 
and at the same instant the point ° 

c is moving perpendicular to be. \\ 

Hence a line through the point b, \ \ 

perpendicular to the plane of the 
paper at the intersection of these \ 

two lines, is at, this instant the in- \ 

stantaneous axis about which the 
two points a and c are moving. 

Their velocities are therefore 
directly as their distances from this 
axis, or 

v.v'v. ab : cb. Fig. 48. 

The same principle may be applied to linkwork in gen- 
eral. The actual velocity of the point a becomes zero when 
the point c reaches the positions 1 and 2, and these points 
are called "dead-points." In the steam-engine the stored-up 
energy of the fly-wheel carries the point c over the dead- 

Connection by Cords. — This connection is principally 
made between blocks, forming a block and fall, or block and 

Although very useful, it is not employed to any extent 
in machine construction. Wire ropes are sometimes used 
instead of belts to transmit power, in which case grooved 
pulleys are required to keep the rope from slipping off. 

Hydraulic Connection. — This is of great importance 
in modern machinery, as the gun-steel is forged by a hydraii- 


lie press, and hydraulic cranes are employed for lifting, the 
heavy weights. The general principle of these machines is 
explained in mechanics, and depends on the fact that if two 
cylinders fitted with pistons are in hydraulic communication, 
the volume of liquid forced out of one is equal to that forced 
into the other. As this volume is the product of the length 
of the cylinder by its area of cross-section, it follows that 
the velocities of the pistons are inversely as their areas. 
From this principle we can obtain a slow motion and great 
power, as in the hydraulic press, or a quick motion and less 
power, as in the hydraulic crane, by regulating properly 
the size of the cylinder. 

87. General Arrangement of Machine-shops — Distribution of 

General Arrangement. — All machine-shops are ar- 
ranged upon the same general principles, though differing 
greatly in details, depending on the work to be done. 

In general, there is first a source of energy, as a steam- 
engine or water-wheel. This source of energy may be 
regarded as the reservoir from which energy is drawn as 
required ; and as different amounts of energy are needed at 
different times, according as different machines are working 
or not, some arrangement must be made to regulate the 
amount of energy. Without this regulation, if several 
machines are suddenly stopped, the energy will be in excess, 
and the remaining machines will increase in speed. This is 
injurious to the work and to the machines. The reverse 
will happen when machines are suddenly started. To regu- 
late the energy of the prime mover, a fly-wheel and governor 
are used. The fly-wheel stores up energy and gives it out ' 
when it is suddenly required, and prevents sudden changes 
in speed, and the governor regulates the supply of steam, 
etc., to the engine. 

The principles are explained in mechanics. 

Distribution of Energy.— To distribute the energy 
from the prime mover to the various machines, any one of 
the methods previously described may be used. Belts are 
generally preferred. 

The pulleys which carry these belts run upon lines of 



•shafting. Extending lengthwise through the shop, there is 
a " main shaft," a, Fig. 49. 

The motion is communicated directly from the prime 
mover b to this main shaft, by a belt. The shaft is supported 
by hangers, c, bolted to the beams or walls. At intervals 
along the main shaft are pulleys, d, each of which carries 
the belt for a particular machine. 

Fig. 49. 

Over each machine is a short shaft, e, called a counter- 

This carries at least three pulleys, the first running loose 
upon the shaft, the second fixed to it, and the third also fixed, 
and driving the machine. Their use has been explained. 

In addition to affording a means of starting and stopping 
any machine without interfering with the main shaft, the 
counter-shaft affords a means of increasing or decreasing the 
speed of any machine, by decreasing or increasing the size 
of the pulleys as compared with those on the main shaft 
which transmit the power. 

88. Machine-tools — Shearing — Cutting — Scraping — drills— Reamers 
and Milling-cutters. 
In every machine the working point, or part by which 
the work is actually done, is called a tool. Machine-tools 



may be classified according to the manner in which they 
act, as — 

1. Shearing-tools; 

2. Cutting or paring-tools ; 

3. Scraping-tools. 

Shearing- tools. — These tools act to divide a plate or 
bar of the material operated on, by causing the parts to 
separate from each other by sliding or shearing. This class 
includes also punches and dies. They are not used to any 
extent in gun-construction. 

Cutting-tools. — These cut a thin chip or shaving from 
the surface of the work and thus produce a new surface. 

Scraping-tools. — These tools scrape off small particles 
from the surface of the work, and correct any irregularities 
that may have been left by the cutting-tool. 

Action of Cutting and of Scraping-tools. — The 
general method of the action of these tools is shown in 
Figs. 50 and 51. 

In each case the tool is acting upon a cylindrical piece 
of work which is rotating in the direction of the arrow. 

The angle DAE is called the cutting angle of the tool ; 
DAC, the angle of relief, the line AC being tangent to the 
face of the work at the point A. The angle CAE is the 
working angle, and is equal to DAC -\- DAE. 

In cutting-tools the angle CAE is always acute; in 
scraping-tools the angle CAE is either right or obtuse : and 
the tools are thus distinguished by their working angles. 

The hook F is given to the tools in order that the cutting 
edge A shall not be above the axis or centre line of the tool. 

If this were the case, any springing of the cutting edge 


I6 5 

■caused by excessive resistance of the material, would move 
the edge A further into the work, or cause it to " dig into " 
it, while as arranged the cutting edge will spring away 
from the work. In plan, the tool may be of various shapes, 
as shown in Fig. 52, these shapes depending on the nature 
of the work. 

ZZS <3 G 

3 C 

Fig. 52. 

Drills and Reamers. — For making cylindrical holes, 
drills and reamers are used. The ordinary drill is shown in 
Fig- 53. the cutting edge being adb; 
the reamer in Fig. 54. 

The reamer consists of a num- 
ber of parallel cutters forming a 
cylinder, and is used to finish a 
cylindrical hole that is required to 
be very true and smooth. Drills 
and reamers rotate about the ver- 
tical axis cd and have generally a 
motion in the direction of this axis. 

Milling-cutters.— These may 
be used to form surfaces of almost o 1 
any shape, and they vary greatly in 
form. The general method of their 
operation is indicated in Fig. 55, in 
which the irregular surface abed is cut by the milling-cutter 
A rotating on the axis B. 

Fig. 53. 

Fig. 55. 

The work C moves along a plane director at right angles 
to the axis B. 



89. Machines in General Use — The Lathe — Parts. 

Machines in General Use. — The machines in generaB 
use are 

The lathe ; 
The planer ; 
The shaper; 
The drill-press ; 
The milling-machine. 

The Lathe. — This machine is intended principally to 
produce accurate surfaces of revolution. Its general ar- 
rangement is as follows: 

A piece of metal or wood is caused to revolve about one 
of its lines as an axis. A cutting- or scraping-tool is made to 
bear against the metal or wood. As the latter, which is 
called the " work," revolves, the tool is caused to move 
either parallel or perpendicular to the axis of the work, or 

Fig. 56. 

in a direction which is compounded of these two motions.- 
The tool cuts a chip or shaving from the surface of the 
work, and by a continuation of its action produces either a 
cylinder, a plane surface, a cone, or any other surface of 



revolution which may be formed by combining the two 
motions at right angles to each other. 

Parts. — The principal parts of the lathe, Fig. 56, are the 
bed, consisting of two parallel ways or guides, a, of a A- 
shaped cross-section. 

On these guides slides the support for the tool, which is 
thus made to travel parallel to the axis of the work. At one 
end of the ways is fixed a heavy block of metal, b, called the 
head-stock. This forms a support for the spindle c. To this 
spindle (see Fig. 57) is attached the face-plate d, by means 
of a screw, d', on the end of the spindle. This spindle is 
hollow at one end, and in this hollow fits a conical piece of 
metal, e, called the live-centre. The spindle also carries a 
speed-cone,/", and a gear-wheel, £". The gear-wheel is fixed 
to the spindle, while the cone revolves freely upon it. The 
gear-wheel^ and cone /may be connected by a bolt, i, pass- 
ing through g. The small end of the speed-cone terminates 
in a gear-wheel, //, which is a part of the cone, and hence 
runs free on the spindle, but revolves with the same angular 
velocity as the cone. Parallel to the lathe-spindle c is an- 
other axis, k, Fig. 57, carrying two toothed wheels, k' and k" . 

Fig. 57. 

This axis k is mounted in eccentric bearings, and may be 
moved so that its wheels, k'k", will engage or disengage with 
those on the lathe-spindle c. The arrangement of the axis 
k and wheels k' and k" is called the back gear. At the op- 
posite end of the lathe-bed is a second block of metal, b', 
resting on the ways, called the tail-stock. It also supports 
a spindle, called the dead-spindle, and this spindle termi- 


nates in a conical piece of metal, e', called the dead-centre or 
back centre. The tail-stock may be moved to any position 
along the ways, and clamped there, and the dead-spindle 
has a sliding motion parallel to the axis of the lathe, which 
enables the distances between the centres e and / to be very 
accurately adjusted. These centres e and, e' , form the axis 
of revolution for any work in the lathe ; and if they are re- 
moved, the prolongation of the axis of the live and dead 
spindles forms this axis. 

90. The Lathe— Slide-rest — Feed— Action. 

Slide-rest. — This forms the support for the cutting- 
tool, and through it motion is given to the tool in any direc- 
tion. It consists (Fig. 58) of a 
slide or bed, /, resting upon the 
ways, a, of the lathe, and ca- 
pable of travelling along them 
by the action of the feed- 
screw m. Upon this slide 
rests a second or cross slide, n, 
58. which moves at right angles 

to the first slide, and hence at right, angles to the- axis of 
the lathe. This cross-slide carries a tool-holder, 0. 

Feed. — The screw m is called the feed-screw. It passes 
through a nut, m' , on the slide-rest, and this nut is made in 
halves which can be separated, thus freeing the nut from 
the feed-screw, and stopping the longitudinal travel of the 
slide-rest. The cross-feed is given by hand or automati- 
cally by gearing, by means of the screw ri. On one end of 
the feed-screw m is fixed the gear-wheel p (Fig. 56). At- 
tached to the lathe-spindle is a second gear-wheel,/', and 
mpon an axis fixed to the head-stock or some convenient 
part of the lathe-bed is a third gear-wheel,/". This ar- 
rangement may be varied according to circumstances, and 
is intended to regulate the velocity ratio of the lathe-spindle 
and that of the feed-screw. Suppose, for example, it is re- 
quired to cut a screw having ten threads to the inch, and 
that the feed-screw of the lathe has this number. Then it 
is evident that the work must turn ten times while the tool 

GUNS. 169 

moves one inch, and also that, in order to move the tool one 
inch, the feed-screw must turn ten times. In other words, 
the velocity ratio of the feed screw and of the work is 
that of equality. Hence, from what has been stated under 
Toothed Wheels, it follows that p and /' must have the 
same number of teeth. The number of teeth upon p" will 
not affect the velocity ratio, since, being a lever of equal 
arms, it receives and transmits the motion from p to/' with- 
out change. 

Action of Lathe. — Motion is imparted to the lathe 
from the belt running on the speed-cone f. By placing the 
belt on the different steps of this cone considerable varia- 
tion of speed may be obtained. If a slower speed than that 
given by the cone is desired, the back gear is used. The 
action of the back gear is as follows : 

When the back gear is in gear with the lathe, the cone- 
pulley is detached from the large gear g by removing the 
bolt, i, Fig. 57. The cone-pulley then rotates, and its small 
gear h drives the large wheel // of the back gear. The 
speed of the back-gear shaft is thus reduced in the inverse 
ratio of the numbers of teeth of h and k' , and with this 
reduced speed the gear k" drives g, which in turn drives 
the lathe-spindle. The speed is again reduced here in the 
inverse ratio of the numbers of the teeth of g and k". 

The action of the feed-screw is evident. By throwing 
the feed-screw out of action and causing the cutting-tool to 
move at right angles to the axis of the lathe by the screw 
n' a plane surface will be formed, and by combining the 
longitudinal and transverse motions in various ways any 
surface of revolution may be produced. 

91. The Planer— Parts— Action. 

The object of this machine is to make a flat surface, 
as nearly plane as possible. Its general principles are as 
follows : 

A large table is made to slide along two parallel plane 
surfaces. Upon this table is fixed the work. Above the 
table the cutting-tool is firmly supported. As the table 
.slides, the tool bears against the work, and cuts a chip or 



shaving, leaving a surface which is an exact copy of the 
parallel plane guiding surfaces of the table. The table and 
work then slide back, and at the end of this motion the cut- 
ting-tool is moved sidewise an amount equal to the width 
of the cut. This side motion is' called the feed. The table 
with the work again moves forward, and the tool makes a 
second cut, and these operations are repeated till the work 
is finished. 

Parts. — The machine (Fig. 59) consists of a bed, a, which 
is essentially two parallel beams or cheeks having on the 

Fig. 59. 

upper surfaces two V-shaped grooves, which are the guide- 
grooves. The table b has two corresponding projections 
on its under side which fit into these guide-grooves. Along 
the middle of the under side of the table is a rack, c, into 
which gears a toothed wheel, d, by which' the table is driven. 
Two vertical standards, e, support a cross-slide, /, and this 
cross-slide carries the tool-holder /' and tool. The cross- 
slide can be raised or lowered upon the standards by the 
screws g, acted on by the bevel gears h. A feed-screw, k t 

GUNS. 171 

runs through the cross-slide, and gives the feed motion 
already spoken of to the tool. ; 

Action.— The machine is driven by two belts passing 
over pulleys, /. As the motion is reversed at every stroke, 
one of the belts is open and the other crossed, as previously 

The gearing is also arranged so that the backward 
movement of the table after the cut is much quicker than 
the forward motion, when the tool is working. This is to 
save time. The action of the machine is automatic both as 
to motion of table and feed, and can be set to any lengih of 
stroke. At the end of the forward travel of the table a pro- 
jecting arm on it moves a lever, and this shifts the belts on 
the pulleys, bringing the reversing-belt into action. At the 
end of the backward motion of the table the feed is brought 
into action, and the tool prepared for its next cut. To pre- 
vent breaking the cutting edge of the tool by dragging it 
over the cut in the backward motion of the table, the tool- 
holder is hinged so that it allows the tool to rotate in the 
direction of the return stroke, but holds it firmly against 
rotation in the opposite direction. The same principle will 
be found later in the rifling-tool. 

92. The Shaper — Parts — Action. 

There are certain objections to the planer which have 
led to the introduction of a modified form of the machine 
called the shaper. For small work, or for short strokes of 
the tool, power is wasted in moving the heavy bed of the 
planer, and when it is necessary to stop the stroke of the 
tool at some definite point, as at a shoulder, it is difficult to 
do this with the planer on account of the delay in shifting 
the belts. The shaper remedies these defects. 

Parts. — It consists of a bed, a (Fig. 60), along which 
slides a head, b. This head carries a ram, c, upon which the 
cutting-tool is fixed. This ram moves backward and for- 
ward at right angles to the bed, and this transverse motion 
is given by a link, d, attached at one end to the ram and 
at the other to an arm, e, upon the toothed wheel/. The 
work is supported upon the tables g or h, as the sliding- 



head may be moved to any position along the bed ; or if 
the work is too long for either table, it is supported at each 
«nd by them, i is an arbor or shaft attached to the bed, 
and intended for cylindrical surfaces. The tables g and h 

Fig. 60. 

can be adjusted vertically by screws, one of them being 
shown at j. 

Action. — The machine is driven by a belt on the speed? 
cone k. Motion is communicated from this cone to a back 
shaft m through the gear-wheel m'. On this back shaft is a 
small pinion splined to the shaft, so that it will slide freely 
along the latter and yet turn with it. The toothed wheel 
/ is driven by this pinion, and this gives motion to the arm 
e, and this to the link d and ram c. A feed-screw, «, is con- 
nected with the sliding head 6, and is driven by the toothed 
wheel m" on the back shaft m. This gears into a pinion on 
the feed-screw, and by means of proper gears any feed can 
be given to the sliding head. 

By this arrangement the sliding head is fed along the 
bed a a certain distance, just before the beginning of each 
stroke. By changing the point of attachment of the link d 
nearer to or further from the centre of e, the length of stroke 
•of the ram may be decreased or increased, and by changing 



its point of attachment to the ram the position of the tool 
may be regulated. The speed is varied by the cones. 
There is also a very ingenious mechanical device invented 
by Sir Joseph Whitworth to cause a slow forward motion 
of the tool while cutting, and a quick backward motion. 

93. The Drill-press — Parts — Action. 

This machine is used for making cylindrical holes of 
comparatively small size. For large sizes, such as the inte- 
rior of tubes, gun-hoops, etc., a boring-mill, or boring lathe, 
is used. 

Parts. — The principal parts, Fig. 61, are the frame a, 
which supports all the parts ; the table b, upon which the 
work is held ; the speed-cone c, which gives motion to the 
drill and the other parts of the machine ; the spindle d, 
which holds the tool e ; the feed-screw/, which gives a ver- 

Fig. 61. 

tical motion to the drill-spindle and its tool ; the feed-shaft 
g, which carries at its lower extremity a hand-wheel, h, and 


at its upper end a pinion, i ; this pinion gears into a toothed 
wheel, k, whose hub or centre forms a nut through which 
the feed-screw / passes ; this wheel and nut are held in a 
collar, so that it can rotate freely but cannot change its po- 
sition vertically ; the bevel gears //' give a motion of rotation 
to the spindle d. 

Action. — When motion is communicated to the speed- 
cone c by a belt, it drives the bevel gear /', and this drives /. 

The hub of the bevel wheel / is hollow, and the drill- 
spindle d passes through it. By means of a spline, the 
spindle can slide freely through the hub of /, but is com- 
pelled to rotate with it no matter what its position verti- 
cally may be. The work rests on the table b, and the tool 
e is in contact with it. As the drill rotates, the tool is 
pressed down upon the work by the action of the feed-screw 
/, which rests upon the upper end of the drill-spindle and is 
connected with it by a collar, so that the spindle can turn 
without causing rotation of the feed-screw. As the work 
progresses, the tool is fed down or pressed down by turning 
the hand-wheel h, which causes the pinion i to rotate, and 
this in turn rotates the toothed wheel k. When the work 
is finished, a reverse motion of the hand-wheel h causes the 
feed-screw f to rise, carrying with it the drill-spindle and 

In all ordinary drills the feed is both automatic and by 

94. The Milling-machine — Farts — Action. 

The milling-machine is a development of the principle 
of the lathe, and is used for forming any irregular surface 
whose elements in one direction are parallel to a plane di- 
rector. In this machine the cutter rotates, while the work 
moves at right angles to the cutter and along a plane sur- 

Parts.— The machine, Fig. 62, consists of the bed a, 
which supports a frame, b, carrying a spindle and cone, c, 
with back gear, d, as in the lathe. To the frame is attached 
a horizontal arm, e, for the support of the outer extremity of 
the axis or arbor of the milling-tool /. This tool is fixed 



upon an axis or arbor, one end of which is supported by 
what may be called the live-centre, and the other end by 
the dead-centre at the extremity of the horizontal arm e. 
Below the cutter is a table, g, which moves at right angles 

Fig. 62. 

to the axis of the milling-cutter. This table is capable of 
adjustment vertically by the screw k, and is fed trans- 
versely by the feed-screw i driven by the worm-gear / 
through the shaft k and cone-pulleys //'. 

Action. — Motion is communicated to the cone-pulley c 
by a belt, and this causes the cutter f to rotate. Feed-motion 
is also communicated to the table g from the cone-pulley c 
through gear wheels to the cone /, and thence by a belt to 
/'. From /' it is communicated to the shaft k which drives 
the worm-wheel/, and this drives the feed-screw i. 

With this machine it is not necessary to have a constant 
velocity ratio between the motion of the tool and that of 
the work, and hence belts instead of gearing are used for 
the feed. Also, since the cut is heavy owing to the large 


tool employed, a slow but powerful feed is required, and 
this is obtained with the worm-gear /. It is evident that 
the profile of the cutter may be of any figure within wide 
limits. Many varieties of these machines are used, and they 
are largely employed in the manufacture of the minor 
parts of small arms. 


95. General Description of Modern Guns— Parts— The Forgings— 
Division of Operations. 

Description. — All modern high-power guns are made 
of steel, and are composed of several parts united to form 
a whole, and the parts are so arranged as best to support 
the stresses upon them. The gun is therefore called a 
" built-up " gun. 

Parts. — The principal parts are (Fig. 63) : the tube, T, 


which iorms the interior of the gun and supports the 
other parts. This contains the powder-chamber, P, and the 
rifling, R. The jacket, J, is the next larger forging, and 
rests upon the exterior of the tube, carrying in rear the 
base-ring in which the threads of the breech-block en- 
gage. The hoops may be divided into two classes, the chase- 
hoops, C and D, and the reinforce hoops, A. The trunnion- 
hoop, T', belongs to the latter class, and there may be one 
or more layers of each class according to the size of the gun. 
The hoops are arranged to break joints when two layers 
overlap, or to lock into each other when stiffness is required, 
as in the chase-hoops. The interior diameters of the jacket 
and hoops are less than the corresponding exterior diame- 
ters of the tube and the parts enveloped. This difference. 

GUNS. 177 

of diameters is called the shrinkage, and its amount, and the 
reason for using it, will be discussed later. These cylinders ' 
are put in place by heating them till they will pass over the 
part to be enveloped, and then cooling them in place. 

FORGINGS. — The manufacture of the forgings and their 
treatment has been explained. At the gun-factory they are 
finish-bored, turned, and assembled to form the gun, and 
after assembling, certain operations are required upon the 
gun itself before it is ready for service. 

Division of Operations. — The mechanical operations 
in gun-building are therefore naturally divided into : 

1. Operations before assembling ; 

2. Operations after assembling. 

96. Operations before Assembling — Tube — Warping — First Boring 
—Tool — Second Boring — Tool. 

Warping. — As received from the manufacturers, the 
tube is liable to be bent or warped, due to the oil-tempering. 

The amount of this warping is ascertained by mounting 
the tube in a lathe, the ends being centred ; and as the tube 
rotates, the deflection at the middle, or at the point where it 
is greatest, can be measured. If found to be considerable, 
it may require a readjustment of the axis of the tube in the 
lathe, or it may be so great as to cause rejection of the tube, 
though this latter seldom occurs. 

First Boring. — The tube is bored before being turned, 
in order that when turned there may be a uniform thickness 
of metal at every point in the same circumference. The 
first boring is done with a tool so arranged that it will run 
straight. This is necessary, because when received the 
bore of every tube is irregular to some extent, and the tube 
is generally warped or bent slightly. The bore must be ex- 
actly parallel to the axis of the lathe, as, in case of deviation 
from this line, the tool may run so far to one side as to spoil 
the tube. A deviation of about 0.25 inch in a length of 
20 feet would reduce the thickness of metal on one side so 
much that the tube would be useless. 

Tool.— The tool used for this purpose is a semi-cylinder 
of cast iron, A, Fig. 64, carrying a cutting-tool of steel, B, in 


front This semi-cylinder exactly fits a hole in the bore of 
the tube, which hole is previously bored very accurately 
with a small lathe-tool. The tool A is supported by a long 

J c 

Frc. 64. 

bar, C, called a boring-bar, which is pushed forward by a 
feed-screw, as in the ordinary lathe. 

The tube is caused to rotate while the tool is pushed for- 
ward ; and since the semi-cylinder A accurately fits the hole 
in the bore at starting, and is constantly forced down against 
it by the presssure of the cut on B, it produces a cylindri- 
cal surface along which A slides, without deviation. The 
length of A, being about three times the diameter of the 
bore, also corrects any tendency to deviation. 

Second Boring.— The first boring gives a straight hole, 
but it is not smooth or regular. It is necessary now to use 
a tool which will remedy these defects. 

Tool. — The tool used for this purpose is called a wood 
reamer. It consists, Fig. 65, of a flat cast-iron head, A, car- 

^ j) a» 


Fig. 65. 

rying two cutters, b b, so that a cut is made at opposite ex- 
tremities of a diameter. DD are two pieces of hard wood 
bolted to the cast-iron head, and turned to a diameter 
slightly greater than that of the hole to be made by the cut- 
ters bb. This packing D, guides the cutters, and keeps them 
steady, and being thoroughly oiled it polishes the bore. 
The cutters are slightly wedge-shaped or conical, so that 








tic. bb. 

they tend always to move towards the axis of the hole 
already bored. By having two cutters, each 
of them does one half the work of a single 
cutter, and hence the tool travels compara- 
tively rapidly down the bore ; and from this 
fact, and also because a light cut is taken, 
and the cutting-edge of the tool is long, so 
that the work is well distributed, it follows 
that the wear of the tool is slight, and the 
bore very smooth and uniform. Fig. 66 illustrates this, be- 
ing exaggerated to show the principle. 

The tool is supported in the same bar, C, and fed forward 
as with the first tool, the tube rotating. 

97. Boring and Turning lathes — Back Bests — Bore of Tube — 

. Turning. 

Lathes. — In all these operations the tube is mounted in 
a boring and turning lathe. These lathes consist, Fig. 67, of 
the bed B, made very strong and much larger than is the 
ordinary lathe ; the head-stock and cone-pulley C; the face- 


-A- ft 




( \r~iT\r 

Fig. 67. 
plate F\ the slide-rest S, carrying a turning-tool; the back 
rests R R, forming intermediate supports for the tube T; 
the boring-bed O, supported on the bed proper, B, and car- 
rying the boring-bar P with its tool Q ; the feed-screw V, 
which lies inside the boring bar P; and the gears W, by 
which the feed-screw is driven. 

Motion is communicated to all the 1 parts by the belt X, 
acting on the cone-pulley. This causes the tube to rotate, 
and also communicates motion to a long shaft, not shown in 
figure, upon the end of which is the lower gear-wheel, W" . 
The motion is transmitted through W to W, and thence to 
the feed-screw V, and bv changing the gears any ratio be- 
tween the velocity of rotation of the tube and that of trans- 


lation of the tool Q can be obtained. The back rests R R 
can be adjusted to any diameter of forging, and the boring- 
bar moved forward or backward. It is necessary that there 
be only one source of motion, since if the feed-screw or slide- 
rest were driven independently of the cone-pulley, a change 
in speed of one would not cause a corresponding change in 
the others, and hence damage to tools, tube, or machine 
might result. 

The slide-rest is driven by a second feed-screw not shown. 

In this lathe, the work may be turned on the exterior 
while boring is in progress. It is best, however, not to 
make a heavy cut on the exterior during boring, as it may 
cause bending of the tube and consequent irregularity of 
bore. Each lathe is supplied with an oil-pump, by means of 
which a stream of oil is forced into the bore while the work 
is in progress. The chips or cuttings come out at the op- 
posite end of the tube from that at which the tool enters. 
The same machines in general are used for boring and turn- 
ing jackets and hoops, with some slight changes necessitated 
by the.. difference in size of the forgings. 

Bore of Tube. — Before assembling, the tube is bored 
below its finished size, as the cooling of the jacket and hoops 
causes irregular contraction of the bore, and metal enough 
must be left to remove these irregularities and give a uni- 
form bore. 

Turning. — After or during boring, the exterior of the 
tube is turned to the proper diameter. The exterior of the 
jacket and hoops is not turned before assembling, as changes 
in these diameters are caused by the shrinkage, and it is 
preferable to finish them after assembling. 

98. Assembling — Furnace — Expansion — Cooling. 

The parts having been turned and bored as explained are 
carefully measured to see that their dimensions are correct. 
A variation of 0.003 m ch is allowed from prescribed diam- 
eters. If the dimensions are correct, the parts are ready for 

Furnace. — The jacket is first placed on the tube. To 
do this the jacket must be expanded sufficiently to allow the 



tube to pass readily through it. As a general rule, an ex- 
pansion of 0.004 inch per inch of diameter is sufficient. 
That is, if the interior diameter of the jacket be 15.00 inches, 
it is to be expanded 

15.00 X .004 = 0.06 inch, 

and the expanded diameter will be 15.00 + -o6= 15.06 

To obtain this expansion the jacket is heated in a furnace. 
This furnace consists essentially of a vertical cylinder of cast 
or wrought iron closed completely except at the top, where 
the forging is introduced and removed. This cylinder is 
surrounded by a fire-box so arranged that the heat shall be 
as uniform as possible at all points. This uniformity of 
heating is essential to prevent warping of the forging and 
consequent difficulty of assembling. The forging is pro- 
tected from direct contact with the fuel, to insure uniformity 
of heating, and also to prevent dirt from collecting on it, as 
this would be difficult to remove. 

Expansion. — The amount of expansion has been stated. 
The heat necessary to obtain this expansion varies slightly 
with different forgings, but ordinarily it 
does not exceed 6oo° F. JJ 

The requisite expansion is determined J\y 

by noting the colors which form on the 
polished surface of the steel, as these colors 
pass through a regular gradation, from pale 
yellow to purple, blue, and black. The 
latter color is seldom exceeded. 

Gauges are also made of the exact diam- 
eter to which the bore should expand. When 
the color indicates the proper expansion, the 
gauges are tried, and when they will enter ^ jtlL 
the bore, the requisite expansion has been 4J— E£P- 

Assembling. — The furnace door is now 
■opened, the jacket hoisted vertically out of 
the furnace by a crane, and placed on a 
•casting, as shown in Fig. 68. This casting stands in a pit of 




Fig. 68. 

1 82 



J T 


Fig. 69. 

sufficient depth to contain the tube. The tube is lowered 
slowly through the jacket till it is in place. 

Cooling. — The heated forging is now 
cooled by the application of water as follows :. 
Fig. 69 shows a section of the tube of 8" 
gun with hot jacket in place ; J is the jacket, 
T the tube resting against a shoulder, C, in the 
jacket ; D is a ring formed of pipe bent into 
a circle, the inside being perforated with 
small holes about f- inch apart. 

This pipe is placed above the shoulder C, 
so that the jacket in cooling may contract or 
" draw " toward this shoulder, and hence in- 
sure a tight joint there. A current of water 
circulates through the pipe, and issues from 
the small holes on its interior against the hot 
jacket. By this means the cooling can be 
readily effected, the ring being gradually 
moved upward, toward the breech, as the 
cooling progresses. It is important that the parts below 
E be cooled first, as otherwise the jacket will grip at E, and 
on cooling and contracting longitudinally, it will compress- 
the tube in this direction, and produce great longitudinal 
strains. The same process applies to hoops, the water being 
applied first at the joint between the cooled and the hot 
hoops, in order to cause contraction toward the joint, and 
keep the latter closed. 

99. Operations after Assembling — Finish-boring — Rifling — Rifling- 
machine — Rifling-tool. 

Finish Boring. — The gun after assembling is placed in 
the boring-lathe, and finish-bored up to the true diameter. 
The wood reamer is used for the final boring. The powder- 
chamber, and the slope connecting this with the bore, are 
also finished. 

Rifling. — The next operation is rifling, or cutting the 
spiral grooves in the bore for giving rotation to the pro- 
jectile. This operation requires a special machine and tool. 

Rifling-machine. — This resembles to some extent the 

GUNS. 183 

boring and turning lathe already described, but differs in 
the following respects : 

1. The gun does not rotate ; 

2. The cutting-tool has a motion both of rotation and of 


Fig. 70. 

Fig. 70 shows the outlines of the rifling-machine. The 
gun is supported on a bed as for boring, Fig. 67, and the 
rifling-bar m is supported as in boring the tube. 

The feed-screw b gives the motion of translation to the 
rifling-bar m and tool g. 

To the side of the rifling-bed is bolted a table, o, which is 
horizontal, and on this table is bolted a " guide bar" e, made 
of flexible steel, and whose shape is that of the developed 
groove of the rifling. A toothed wheel or gear, c, is fixed to 
the rifling-bar, and a toothed rack, d, engages with this gear. 
At the outer end of the rack are two small rollers, //', em- 
bracing the steel guide-bar e. The rifling-bar m is free to 
turn about its axis while moving forward. 

The action is as follows : When the rifling-bar is driven 
forward by its feed-screw b, it carries with it the toothed 
rack d. 

The outer end of this rack travels along the guide-bar e, 
and as the roller /bears against this guide-bar, the rack is 
pushed inward or to the left in the figure. This causes the 
gear c to rotate to the right, carrying the rifling-bar with it, 
and thus the rifling-tool is caused to cut the proper groove 
in the gun. 

Rifling-tool (Fig. 71). — This is a cylindrical head, c, ol 
metal accurately fitting the bore. Four radial arms, d, slide 
in grooves in the front face of the cylinder, and carry the 
cutters k on their outer ends. 

1 84 


The inner ends rest on a wedge, e, which has a sliding 
motion parallel to the axis of the cylinder. By sliding this 
wedge forward the radial arms and cutters are pushed out, 
and by sliding it backward they are pulled in. By this 
means the depth of the cut or feed is regulated. 

Fig. 71. 

When the tool reaches the end of the groove in the gun, 
the projecting end of the sliding wedge strikes a rod, r, in 
the bore, and the cutters are thus drawn back, which pre- 
vents breaking them by dragging them over the cut ; the 
motion of the machine is then reversed and the tool drawn 
out of the bore. As the rifling-bar and tool move forward, 
a stream of oil is forced on the cutters, by a pump. 

Arriving at the end of the cut, the cutters are automati- 
cally withdrawn as explained; and as the motion of the 
rifling-machine is reversed the bar and tool return, being 
guided in their return motion by the bearing of the roller/', 
Fig. 70, upon the outside of the guide-bar. The sliding 
wedge is then adjusted for the next cut, and pushed out to 
the front, raising the cutters, and so on till the groove is fin- 
ished. To cut the next groove, the rifling-bar is turned in 
its bearings a distance equal to the width of one land of the 
rifling, and the new groove cut as above described. 

The remaining operations are finish-turning, inserting the 
breech- screw, fitting the mechanism, marking, and weighing, and 
are not different from the ordinary operations of a machine- 




100. Definitions — Case Considered — Radial Stress and Strain. 

Definitions. — In the following discussion stress means 
the force acting in pounds or tons per square inch, and strain 
the effect of this force ; this effect being either extension or 
compression, and expressed in inches per inch of length. 

Elastic Strength. — The elastic strength of a cylinder or 
gun is the greatest stress to which it can be subjected 
without straining any part of the cylinder or gun beyond its 
elastic limit. 

Case Considered. — To show the stresses acting upon a 
cylinder, and the strains produced by them, let us consider 
the case of a single cylinder, closed at both ends, and acted 
upon by an interior pressure only, the exterior pressure 
being that of the atmosphere, and consequently so small 
that it may be neglected. This case corresponds to that of 
a gun composed of a single piece of metal, closed at one end 
by the breech, and at the other by the projectile, and acted 
on by the pressure of the powder-gas. It is evident that a 
normal stress is acting upon all parts of the interior of this 
cylinder, including the ends. 

Radial Stress and Strain. — Take a ring of this cyl- 
inder, whose length is unity, Fig. 72, and consider a cube of 
this ring whose edges are unity. 

Let p represent the normal 
stress upon the inner surface of 
this cube. Then the effect of 
this stress is to compress the 
cube in the direction of the 
radius, and to decrease the thick- 
ness of the wall of the cylinder. 
It also increases the length of 
the radius. Since the same is 
true for every unit-cube into 
which the ring may be divided, Fig. 72. 

we conclude : 

(1) That one effect of an interior stress upon a closed 


tube is to strain the wall of the tube in the direction of the 
radius ; 

(2) That this stress decreases the thickness of the walls 
of the tube, and increases the interior radius, 

This is called the radial stress, and its accompanying 
strain is the radial strain. 

It must remembered that for the particular case con- 
sidered the effect is as stated. But we may have both an 
interior and an exterior stress acting at the same time, or 
we may have an exterior stress acting alone, the interior 
stress being zero. 

According to the relative values of the stresses acting 
we may have therefore a radial strain of extension or of 
compression, as will be shown later. 

101. Tangential Stress and Strain — Longitudinal Stress and Strain 
— Conclusions. 

Tangential Stress and Strain.— Consider again the 
same ring of metal as before, whose length is unity, and take 
any particular unit cube, as a, Fig. 73. 

The stress p acts normal to 
the diametral plane be, and its 
effect is to separate the cylinder 
into two halves along this plane. 
Hence the edges of the cube a 
parallel to the direction of the 
stress or normal to the plane be 
are strained by this stress, and 
this is true for the whole cube; 
Fig. 73. hence the effect is to elongate 

the cube in this direction. This 
is called the tangential or circumferential stress, or the 
hoop tension, and it produces a corresponding strain. Its 
amount is obtained by multiplying the intensity of the 
stress by the area over which it acts. The intensity is 
p, and for each side of the ring the area over which it 
acts is r X 1 = r. Hence the resultant tangential force 
is pr. This force is resisted by the elasticity of the fibres, 
and it produces a corresponding stress in these fibres, 
which at any point is represented by t. Since the 

GUNS. 187 

same may be shown for each of the unit cubes, the total 
effect of this stress is to strain or elongate the interior cir- 
cumference of the cylinder in the direction of the tangent. 
This also increases the length of the radius. Hence we 
conclude : 

(1) That another effect of the interior stress upon a closed 
tube is to strain the wall of the tube in the direction of the 

(2) That the stress increases the interior radius of the 

As in the case of the radial stress, it must be remembered 
that this stress may decrease the circumference of the interior 
layer, or shorten the radius, depending upon the resultant 
of the forces acting. 

It appears from the above discussion that the radius is 
changed by both the radial and the tangential stresses, and 
the two cases must not be confused. 

Longitudinal Stress and Strain. — In addition to 
the radial and tangential stresses acting on the unit cube, 
there is a third stress due to the pressures on the ends of 
the cylinder. This stress acts parallel to the axis of the 
cylinder, and its effect is to strain the elementary cube in 
the direction of this axis. Since this is true for each cube, 
the resultant strain is an elongation of the tube in this direc- 

This is called the longitudinal stress, and it produces a 
corresponding strain. 

Conclusions. — If we follow the same method of discus- 
sion for the case of an exterior and an interior stress acting 
at the same time, or for the case of an exterior stress acting 
alone, the interior stress being zero, similar results will be 

Hence we conclude in general that when a single cyl- 
inder is acted on by exterior and interior stresses, their effect 
is to produce in the cylinder : 

1. A radial stress,/, and.its corresponding strain ; 

2. A tangential stress, t, and its corresponding strain; 

3. A longitudinal stress, q, and its corresponding strain ; 


and that all these stresses exist at the same time and at 
every point of the cylinder. 

102. Relations between Stresses and Strains when all the Forces 
are Tensions — Application to Cube in Gun-cylinder. 
Relations between Stesses and Strains. — Since all 
the stresses /, t, and q exist at the same time, and each pro- 
duces its own strain, it is required to find the resultant strain 
due to these three stresses acting together. 

For this purpose it is more simple to consider at first, 
three stresses of the same kind. 

If a cubical elastic solid be acted on by a given stress in 
a direction normal to one of its faces, experiment shows 
that it produces a corresponding strain in that direction, 

and that it will also produce con- 
trary strains in the two direc- 
tions at right angles to the first, 
equal to one-third the first strain. 
Thus, Fig. 74, if the force / act 
on the cube in the direction 
shown, it will elongate the edges 
act, bb, etc., and will contract the edges ac, ab, and this con- 
traction will be one third the elongation of aa, bb. 

This law holds only within the elastic limit. Consider 
the general case of a cube acted on by the three stresses X, 
Y, and Z, at right angles to the faces of the cube, and sup- 
pose these stresses to be tensions. 

Let A be the resultant strain in the direction of the stress 
M, that in the direction of Y ; 
v, that in the direction of Z; 
-£„ the modulus of elasticity of the cube. 
The stress X, by a preceding principle (see equation 
(169)), produces a strain in its own direction equal to 


The stress Y decreases this strain by the amount 



and the stress Z by the amount 

Hence the total strain in the direction of X is 



In the same way we have for the total strains in the 
direction of Fand Z 




3 ' 

Application to Cube in Gun-cylinder. — Referring 
now to the unit cube in the gun-cylinder, we have the same 
case, except that one of the stresses is a compression. 
Hence, substituting in the above equations t for X, — p for 
Y, and q for Z, we have 



In these equations A. is the strain in the direction of the 
circumference or tangent, }i the strain in the direction of 
the radius, and v the strain in the direction of the axis of 
the cylinder, due to the action of the three forces p, t, and q 
at any point. These strains may be extension or compres- 


sion according to the relative values and directions of the 

103. Lamp's First Law Connecting t, p, and q. 

In equations (170) the values of A, /x, and v are unknown, 
and they are expressed in terms. of t, p, and q, which are also 

Hence in order to find the values of A, jx t and v in known 
terms it is necessary to establish certain equations of condi- 
tion, by means of which t, p, and q may be replaced by 
known terms. This has been done by what are known as 
Lame's formulas, from the name of the distinguished in- 
vestigator of the subject of the elasticity of solid bodies, 
M. Lame. 

To deduce the first law it is assumed that the longitu- 
dinal stress q is constant throughout the cross-section of 
the cylinder. 

This is not exactly true, but the results obtained upon 
this hypothesis are sufficiently exact in practice. 

Assume the last of equations (170), 



In this equation q is constant by hypothesis, and the 
value of v varies only with t and p. One third of the dif- 
ference of these quantities is the only variable in the above 
equation ; and since t and p vary together at different points, 

t — p 
the variations in the value will be small, and may be 

neglected in comparison with q. 

Hence we may assume without material error that v is 
constant throughout the cross-section of the cylinder. 

From this we have 

t—p— l{q — v£ t ) = constant, . . . (171) 

t —p — constant (172) 

GUMS. 19 » 


',-4lr,-% <*> 

in which T„, P , T x , and P, are the values of t and / at the 
interior and exterior of the cylinder respectively. 

From this we have Lamp's First Law : 

The difference between the tension and the pressure is the 
same at all points. 

104. Lamp's Second Law. 

The second law, or second equation of condition for^, t, 
and q, is deduced as follows : 
In Fig. 75 

Let R , be the interior radius of the cylinder ; 
J?,, the exterior radius; 
r, the radius of any circle of the section ; 
r', the radius of a circle of 
the section, exterior and 
near to that whose 
radius is r ; 
p, t, and q, the radial, tangential, and 
longitudinal stresses, re- 
spectively, at any point 
of the circle whose 
radius is r ; 
P„ and T„ the values of p and t for 'Fig. 75. 

the interior of the cylinder ; 
P x and T lt the values of p and t for the exterior of the cylia 
der ; 
q, constant for all parts of the cross-section ; 
E a , the modulus of elasticity. 
Consider the cylindrical ring whose radii are r and r 1 
and whose length is unity. 

The interior pressure p, as previously shown in the dis- 
cussion of tangential stress, produces a tangential stress on 
the interior of the ring equal to pr. 

For the circle whose radius is r' the pressure / becomes 
p', and the force causing tangential stress on the exterior of 
the ring is p'r' . 


There is therefore a difference in tension between the 
two parts of the ring equal to 

p'r' — pr, 

and this difference of tension is balanced by the product of 
the thickness of the ring r' — r, and the mean stress along 
bb', or along any other part of its thickness. 

We have therefore the following equation for the whole 
ring, since the tension and pressure have opposite signs. 

2/V — 2pr = — 2r{r' — r), . . . . (174) 

r being the mean stress throughout the thickness of the 
ring. From which 

p'r 1 — pr _ 

r — r 


Passing to the limit by making f = r, in which case r 
becomes t, we have 

«-*<*(£^l„-^- ■ • (■*> 

limit of (— T) r , = r =— t 077)' 


^ = -< o*v 

From (171) we have 

t=P+Z{q-vE t ) (179) 

Substituting the second member for t in (178), we have 

-^- = -P-i{q-vE^ (180I. 

Differentiating ; p and r being variables, 
pdr -|- rdp 


= -P-fa-y£d ( l8l > 



GUNS. I93 

dr dp 

r zp + zia- "£„) 



2 ^ge [2/ + fa - vE a )] + logeC. . (183) 

Substituting the value of p + $(q — y£ ) from (179), we 

C\t+P), (184) 


From which we can write 

{t -\-py = -pr; = constant. . . . (185) 

{t+py = {T t + P.)R? 
{t+f>Y = {T l +P l )R l * 


and from these we have Lame's Second Law : 

The sum of the tension in the direction of the circumference, 

and of the pressure in the direction of the radius, varies inversely 

as the square of the radius. 

Formulas (172) and (185) are known as Lame's formulas. 

105. Curve of Stresses in a Cylinder — Discussion. 

Lame's formulas enable us to determine the stresses ex- 
isting at every point of the cross-section of a cylinder sub- 
jected to the action of exterior and interior forces. A curve 
showing the relation between the radii and the stresses for 
all points of the cross-section is called a curve of stress, and 
is thus determined. 

Assume equations (173) and (186) : 

(*+pY = (t. + p,)r;; 

t-p = T.-P,; 
{t+pY = {T 1 + P l )R l t ; 
t-p = 7", - p. 


Combining these equations, and eliminating T t , T , and 
p, we obtain 

PR-— PR* R *R HP — P ) i 

r?-r* ~*~ r;'-r* r"' ' ' v 7; 

Combining again and eliminating 7", , Zj, , and ^, we have 

p r; - P& r:r;{p„- p,) i 

p - r:-r: "^ r?-r: f • ( - I&6 '' 

Since ^ is assumed constant throughout the cross-section 
it is not considered in this discussion. 

Equations (187) and (188) give the values of t and / at 
any circumference whose radius is r. From these equations 
we can construct the curves of stress. To illustrate, take 
equation (187). 

Differentiating, we have 

dr -~ r:-r; • • • • 089) 

d L _ 2R>R >(P-P 1 ) i 


Differentiating (189), we have 

dr* ~ R* - R* r k 


From (187), we have for the values of / for the interior 
and exterior of the cylinder, by making r = R and r — R,, 

T - p ( £' + V) _ P ^EI-_. (lQl) 

1 ' - ^' R? - R„' iRS-R, 1 ' • ' V gI) 

t-p _i^!_ _ P (K + K) . 

1 ~~ • R t ' - R c ' ■ r; -r, 2 ~ ■ ' K9 > 

Now considering the two forces P t and P, , we may have 
the following cases : 

1. P\>P,\ 

2. />. = />; 
3- P. < P, 

First. P a > P,. 



Equation (189) shows that — <o; hence t decreases 


•algebraically as r increases. Equation (190) shows that 

-n > o ; hence the curve 01 stress is concave upwards. 

■dr r 

If we lay off values of r along the axis OX, and of t along 
OY, the resulting curve will be the 
curve of stress for the particular 
stress considered, and may be any 
one of the curves b, d, c, a in Fig. 
76. If T e and T x are both positive, 
we have curve b, which is the gen- 
eral case. If T = — T x , we have" 
curve d. If Tj, = o, we have curve c. 
If T„ and T, are both negative, 
we have curve a. 

Second. P t -= P t . 

In this case 


d l t 

d? = °' d? = °< 

and the curve of stress becomes a 
right line parallel to the axis of OX. 

Equation (191) shows that T„ < o, Fig. 76. 

and hence the right line will be below the axis of OX, as 
in Fig. tj. 

Fig. 77. 

Fig. 78. 



Third. P <P,. 
In this case 


>o, ^<o, 

hence t increases algebraically with r, and the curve is 
convex upwards. Equation (191) shows that T < o, and 
hence the curve will be as in Fig. 78. 

106. Conclusion from Curves — Method of Strengthening Cylinder. 
Conclusion. — Similar results will be obtained by dis- 
cussing equation (188), and an examination of all the curves 
thus obtained will show that in general the greatest stresses 
are at the interior of the cylinder, and the object of modern 
gun-construction is to strengthen this interior layer. 

Method of Strengthening Cylinder. — Take a gun 
composed of one piece of metal, such as the old cast-iron 
guns. When fired, the interior pressure is 
P t , and the exterior pressure is zero, since 
the pressure of the air may be neglected. 

Then /'„>/',, and the curve of tensions 
is b, Figs. 76 and 79. If P is great, the 
inner layer may be deformed or ruptured 
before the exterior layers are brought to 
their limit of endurance. Suppose, how- 
ever, that before firing we cause a pressure, 

Then we have 

Fig. 79. 

P^ , to act upon the exterior of the cylinder, 
the case where P < P lt and the state of 
stress in the cylinder before firing is as in 
Figs. 78 and 80. That is, all the layers 
are compressed, those at the interior 
more than those at the exterior. 

Now when the gun is fired, we have 
the condition P c > P Jt and the curve of 
tensions Would be b, Fig. 79, were it not 
that we have already a curve of tensions,/, 
Fig. 80, in the cylinder. 

Hence the new curve of tensions is the resultant of the 
two curves b and/, or AB, Fig. 8:. 



That is, before the inner layer can be put in tension, a 
force must be exerted sufficient to overcome the preliminary 
•or initial compression, and after this any 
excess of the force will produce tension. 
The result is shown in Fig. 81. A'B' 
is the curve of tensions, supposing no 
previous stress acting on the cylinder. 
CD is the curve of initial compression ; 
AB is the resultant curve, which is ob- 
tained by taking differences of ordi- 
nates, and is the curve representing 
the actual tensions. 

This method is called the method of 
initial compression, and is now universally used in gun-con- 

107. Values of the Strains at any Point in a Cylinder in Terms of 
the Radii and Pressures. 

The general laws of the stresses in a cylinder have been 
determined, and the curves of stress constructed. The ob- 
ject of the present discussion is to find the values of the 
strains ^, M, an d " at any point in a cylinder in terms of the 
exterior and interior pressures and radii, and of the modulus 
£ , these strains being within the elastic limit of the metal. 

For this purpose assume equations (170) : 

Fig. 81. 


It may be shown analytically, and the result has been 
proved by actual experience in gun-building, that in con- 
sidering the resistance of the cylinder we can simplify the 
problem by neglecting the longitudinal force q, and consid- 
ering at first only the forces t and p, and afterwards con- 
sider separately the force q, when the longitudinal strength 


of the gun is to be determined. This is equivalent to mak- 
ing q = o in the above equations. These equations then . 


»=-Up + 



Substitute the values of t and p from (187) and (188) in 
(193), and we have 

_ 2 {p a R; - pa*) ar;r:(p, - p.) 1 , .. 

A - 3 (^ a - R?)E. ^ 3(^, 2 - R:)E» r> ' ^ W 

2{Pfi:-p l R?) ar?r:{p -p,) i 

M - 3{R; - R ')E 3(K - R:)E, r> ' ^ 95 > 

2(p r:-p,r?) 

v =~ 3 (r;-r;)e;- (^ 

These equations are general and give the values of the 
strains A., jx, and v at any point r in a cylinder. 

To find the values of the strains at any particular point 
we substitute for r the value of the radius at that point. 

Thus for the interior of the cylinder, substitute ^ for r y 
and for the exterior R t for r. 

108. Maximum Values of Strains in a Cylinder. 

If any part of a gun-cylinder is subjected to a stress- 
beyond its elastic limit, this part becomes deformed. 

Hence other parts will be called upon to bear stresses 
different from those for which they were calculated, and 
the result will be that after a few rounds the whole structure 
may be deformed or destroyed. We then use the following 
principle, which is the foundation of the modern theory of 
gun-construction : 

No fibre of any cylinder in the gun must be strained, under 
any circumstances, beyond the elastic limit of the metal of that 

GUNS. 199 

From this principle we can determine the maximum 
stress to which a cylinder can be subjected. 

It has been shown that the inner layer of a cylinder is 
subjected to the greatest stress. Hence if this layer does 
not pass its elastic limit, every other layer, and consequently 
the cylinder itself, will be safe. 

The strains at the inner layer will be obtained from (194) 
and (195) by making r — R . Considering for the present 
only A. and /<, since v is constant, we have, making r = R , 

_ (4R;+2R I> *)P -6R,>P 1 

l{R:-R:)E a ^ 97 > 

"-- 3 (ie,- -*.■)/?. • • • (I98) 

These are any strains within the elastic limit. 

Let d be the elastic limit of the cylinder for tension ; 
p a , the elastic limit for compression, in pounds or 
tons per square inch. 

Then, by equation (169), the elongation at the elastic 
limit will be 


and the compression at the elastic limit 

and, by the principle previously stated, these are the 
maximum strains that can be allowed. Since, in general, A. 
is extension and m compression, A. and n must be equal to 

ft n 

—- and -^r, respectively, at the limit. If, however, A becomes 
compression and // extension, A. must be placed equal to 


~, and m to -= L f as will be seen later. We have then, equat- 
£<> ^0 

ing these values, 

*-£,- hr^-r^e, ' ■ ■ ■ (l99) 


*- E.- 3 {R'-R')K ' ' - (m 

109. Limiting Interior Pressures— Discussion. 

Limiting Interior Pressures, — Solving (199) and (200) 
for P Q , we find the pressures which will produce the strains 

X = -£■ and ft = -—-, and these will be the maximum interior 

pressures which the cylinder will stand. These values are 

^•-— 4ie,»4- 2 ^ ' • • ■ (20I) 

3^ -*.>. + 2 jg,-/> 1 

^" _ 4», J -2ie o a • • • • <202) 

P o will cause the inner layer of the cylinder to elongate 
till it reaches the elastic limit O , and P op will cause the 
inner layer to be compressed radially till it reaches th? 
elastic limit p a . 

These values of P t e and P& will differ, and the smallei 
value marks the limit of stress to which the cylinder can b«, 
safely subjected. 

For instance, if P„e < P of , , the limit 0„ will be reached, 
while that for compression p a will not be. The cylinder has 
therefore more compressive strength than can be used* since 
if we increase P„ e till it is equal to P 0O , we pass the limit 0, , 
which is contrary to the principle stated. 

Discussion. — In a single cylinder the most common case 
is that in which P t , the exterior pressure, is that of the 
atmosphere, and may be neglected. P 1 is therefore zero> and 
under this condition equations (201) and (202) become 

D 3 (R> - RM 


4^ + 2^' 

° p ~ 4R?-~2rT t 204 ' 

Since for all metals used in gun-construction 8, = or < 
P„ P a » will always be less than />„., and hence, it alone will 
be considered. 

GUMS. 20 1 

(1) Required the thickness of wall necessary to resist a 
given interior pressure P, e - Solving (203) for (J?, — R ), the 
thickness, we have 

(2) To show the relation between the thickness of the 
cylinder and its resistance, we have from (203) 

3(1 - §->. 
P>» = ^— (206) 

Suppose the cylinder to be one calibre thick. Then 

*. =3*., 

p„« = .6 3 o . 

If the cylinder be of infinite thickness, R l = 00 , and 

which shows that an increase in thickness from one calibre 
to infinity, increases the strength of the cylinder only from 
.6 3 o to .75^. 

Hence we conclude that a single cylinder is not materi- 
ally strengthened by increasing its thickness beyond one 
calibre, and also that the greatest possible value for the 
interior pressure in a single cylinder without initial com- 
pression is less than 


110. Limiting Exterior Pressures — Thickness of Cylinder — Exterior 
' Strains. 

Limiting Exterior Pressures. — It has been shown 
that, in order to strengthen the cylinder, we apply an exte- 
rior pressure P l , and produce a compression of the cylinder, 
this compression being greatest at the interior. 

What is the limiting value of this exterior pressure? 

Its limiting value is that which will compress the inner 
layer up to its elastic limit ; and it is determined as follows: 


The interior pressure being zero, or P, — o, the strains \ 
and M at the interior become, from (197) and (198), 

-2R*P, . , 

.... (207) 

(r; - r;)e. ' 

3^ - r?)e; 


The first, being negative, shows that the inner layer is 
compressed tangentially ; the second, being positive, that 
the wall of the cylinder is extended in a radial direction or 
increased in thickness. As before, the limiting compressive 
strain is 


and that for extension 


and the values of A. and p must not exceed these respectively. 

P ,_ - 2 r;p 1 

A ~~£. {r;-r;)e.' 

, 2R,'P, 

** - E a ~ 3 (r; - r.-)e; 

Solving for P„ we have 

"• 2R, 

. . (209) 

r * — ,s" • • • 

. . (210) 

The negative sign is omitted in (209), as it indicates com 
pression simply. These equations are useful in determining 
the limiting value of the exterior pressure which the tube or 
inner cylinder will support, when we are considering what 
pressure P, can be applied to its exterior to strengthen it; 

G UNS. 203 

and since P lP is generally less than P l9 , equation (209) only is 

Thickness of Cylinder to Resist External Pres- 
sure. — From equation (209) the thickness of wall of cylinder 
necessary to resist a given exterior pressure P )9 may be 

Solving it for R t — R t = H' , the thickness, we have 

R >- R ° = H ' = R {\/j-^p;,- 1 )- • (2II) 

Strain at Exterior of Cylinder. — The only strain 
of importance at the exterior of the cylinder is that in the 
direction of the circumference, or X. Referring to the gen- 
eral value for it at any point r, equation (194), and making 
r = R i , we have for its value at the exterior 

3 {r>-r;)£ • ' • • K2l2) 

When P. = o, 

a contraction. 
When P, = o, 


X = (*,• -r})e. (2I4) 

an extension. 

111. Longitudinal Strength. 

To determine this, suppose the cylinder closed at one 
end by the breech, and at the other end by the projectile, as 
in a gun. The total pressure acting on the bottom of the 
cylinder is then 

7rR 'P a . 

The area of cross-section of the cylinder is 

n{R; - r,% 


and the pressure reR 'P is resisted by the elasticity of this 
cross-section. Supposing the pressure to be uniformly dis- 
tributed, the stress per unit area of cross-section is 

„ *r:p* _ p ^ (2l 

q - ti{r?-r:)- R?-Rr ■ ■ • y 5) 

Substitute in the third of equations (170) for t and / their 
values from (187) and (188), and for q its value from (215), 
and we have for the value of the strain v in the direction of 
the axis of the cylinder, 

PR*— iP R * 

-=tral <*■«> 

The maximum value of this strain must be equal to 
-=- as before, hence 

v ~ e, ~ 3 {R t ' - r:)e; 

Solving for P„, we have 

3(*,« - R.y>. + 2r;p x 

■* 00 E> J ' 

If P, = 0, 

• 3(^-W 



For the thickness of wall necessary to resist the pressure 
P, acting parallel to the axis, we have, solving (218) for 
-^1 — Ro » 

R,-R = H" = Ro(\/ P °° + m - i\ • (219) 

This discussion applies to the older guns made of a single 
piece of metal. With modern built-up guns the breech- 
block is in an outer cylinder or jacket, and a new formula 
must be deduced for the longitudinal strength in such a gun. 

G UNS. 205 

112. General Principles of Built-up Guns— Method of Applying Ex- 
terior Pressure. 

General Principles.— It has been stated, in discussing 
the resistance of a single cylinder, that it may be strength- 
ened by applying a force P l to the exterior of the cylinder. 
This force, as shown, produces a compression of all the lay- 
ers of the inner cylinder, the interior layer being compressed 
to the greatest extent, as it should be, since it is extended 
more than any other layer by the action of the powder-gas. 

The layers of the cylinder being thus subjected to tan- 
gential compression, this compression must first be over- 
come before the inner layers can be brought to a state of 
tension. Hence part of the powder-pressure is exerted to 
bring the inner layers to a neutral state of strain, and any 
excess of pressure over that required for this purpose will 
cause tension in the inner layers. It is evident, however, 
that since the cylinder will safely support a certain interior 
pressure P a9 or P oP without this preliminary compression, it 
will support a much greater interior pressure with the aid 
of this compression. 

Method of Applying Exterior Pressures. — The 
method of applying this exterior pressure is by placing over 
the inner cylinder an exterior one, whose interior diameter 
is slightly less than the exterior diameter of the inner cylin- 
der. The exterior cylinder is applied as has been explained 
in Gun-construction. Upon cooling it contracts upon the 
inner cylinder, and if the difference of diameters is properly 
regulated it will produce the required pressure. 

It is evident, however, that in compressing and strength- 
ening the inner cylinder, the outer cylinder is itself extended 
and weakened ; but this extension or weakening of the outer 
cylinder, when properly regulated, can be supported with- 
out damage to the structure. 

According to Lame's second law the sum of the tension 
and pressure varies inversely as the square of the radius. 
Hence a value of (T„-\-P a ) which would be large at the 
interior would be very much diminished at the radius R t . 
This principle is applied to any number of cylinders placed 
one over the other. The differences of diameters of any 



two adjacent cylinders is called " the shrinkage," the re- 
sulting gun a built-up gun, and the cylinder a compound 

113. Calculations for Compound Cylinder — States Considered — 
Calculations. — Suppose the cylinders assembled with 
the proper shrinkage. It is required — 

i. To calculate the maximum resistance of the com- 
pound cylinder ; 

2. To calculate the shrinkage, so that when assembled 
the pressure exerted by the exterior upon the interior cyl- 
inders shall be such as to give to the compound cylinder its 
maximum resistance. 

States of Cylinder. — When the powder-pressure is 
acting, the cylinder is said to be "in action;" when the 
powder-pressure ceases to act, the cylinder is " at rest." It 
is evident, however, that the system is not free from stress 
when at rest, owing to the shrinkage; and it is necessary to 
consider the stresses both in action and at rest, as will be 
seen later. 

Nomenclature. — For simplicity of discussion, consider 
that the compound cylinder is made up of two cylinders 

only. The inner cylinder will be 
designated as the tube, and the 
exterior as the jacket. 
In Fig. 82 let 

, R, be the radii of the inte- 
rior, middle, and ex- 
terior surfaces of the 
cylinders, R, being, 
the radius of the sur- 
face of contact be- 
tween the tube and 
jacket ; 
P lt the normal pressures at 
and exterior surfaces, re- 

-#„> -^i 

Fig. 82. 

the interior, 

P P 


spectively, when the system is in action ; 
A> > A > A > variations in P , P lt P,, produced by any cause 

G UNS. 207 

whatever, such as a change from a state of 
action to that of rest ; 
(t , 8 l , elastic limits of tube and jacket, respectively, for 

tension ; 
p , p lt same for compression; 

E a , E lt moduli of elasticity of tube and jacket respec- 
tively. These are generally assumed as equal, 
hence E„ = E t ; 
P/, the normal pressure acting at the surface of con- 
tact of the two cylinders when the system is at 
For a single cylinder the radii have been denoted in the 
previous discussions by R and ./?, , and the pressures by P 
and P x . 

As a general rule, if n denote the number of the cylinder, 
counting from the interior, its radii and pressures are n — 1 
and n, for the interior and exterior respectively. Thus, for 
the fourth cylinder we have R a , R t , P„ and P„ and by 
applying this rule the equations deduced for two cylin- 
ders may be applied to any number. 

114. Resistance of Compound Cylinder in Action. 

In the case of a compound cylinder in action the tube 
is acted on by an interior pressure P„ and by an exterior 
pressure P t . The jacket is acted on by an interior pressure 
P, and by an exterior pressure P„ which is that of the at- 
mosphere, and therefore regarded as zero. The jacket is 
therefore a single cylinder acted on by an interior force, P u 
and its resistance is given by equation (203). 

Making, in (203), 

we write 

= *., 


= »,. 


_ 3W 







P lt being alone considered, because, as previously shown, 
it is always less than P xf . (See equations (203), (204).) 

This pressure P,e will extend the inner layer of the 


jacket to its elastic limit, and hence it is the greatest 
pressure which can be safely applied to the interior of this 

The pressure P l9 just found also acts upon the exterior 
of the tube, and P acts upon the interior. Hence we have 
the case, already 'discussed, of a cylinder acted upon by two 
forces, and equations (201) and (202) apply, viz., 

^- 4^ + 2*.' ' ' * ' ( } 

°" 4R?-2R? k > 

The smaller value must be selected, and this value 
marks the limiting pressure which the tube, and conse- 
quently the compound cylinder, will safely support. 

When this interior pressure acts, it raises the inner layer- 
of the tube to its elastic limit for tension or compression^ 
according as P a % or P ap is the less. At the same time it 
produces the pressure P^ at the surface of contact. Hence 
when the maximum interior pressure is acting it raises the 
inner layers of both cylinders to their elastic limits. 

Equation (220) is solved first, since it contains only known; 
quantities in the second member. The resulting value, P lty 
is then substituted in both (221) and (222), and both of these 
equations can then be solved, the smaller value being taken 
as explained. 

Collecting these equations for convenience, we have for 
calculating the maximum pressures which a compound 
cylinder composed of a tube and jacket will safely support 
in action 

jf>_ 4R* + 2R, • ^ 220 > 

"" — 4^' — 2R' ■ • . • \my 

GUNS. 209 

115. Longitudinal Strength of Compound Cylinder. 

In a gun composed of two cylinders the jacket carries 
the breech-block, in order to free the tube as much as pos- 
sible from longitudinal stress. 

The total pressure upon the breech-block is, as before, 

This acts upon the area of cross-section of the jacket, 
which is n(R? — R?) ; hence the stress per unit area of this 
cross-section is 

*&:p. _ p»r: ,, 

q - n{R? - r;) ~ R* - r* { 3) 

The values of t and p from (187) and (188) become for 
the outer cylinder, by making the following changes in the 

P, = P llt R. = R l ; 

P s = 0, R, = R, ; 

_ P«R? , W^i , , , 

R? - R?~T~ RS - R* r° {224) 

p i9 r; R; R?p lt 1 

Substituting these values of t, p, and q in the third of 
equations (170), we have 

V ~ 3(R*-R l t )E l K } 

The maximum safe longitudinal strain upon the jacket is 
~. If the value of v calculated by (226) is less than this, 

the jacket will not be overstrained longitudinally by P . If 


greater than -=r-, the pressure P, must be reduced. 

The limiting value for the pressure is obtained, as before,, 
by placing 

0, iP a R? - 2P X «R? 

v = 

E, - 3(R; - R?)E, ■ 


Solving for P a , we have 

~^r; • • • • (22? > 

116. The System at Rest — Reasons for Considering It — Variations 
of Pressure. 

The formulas previously deduced give the maximum 
pressures which the compound cylinder will safely support 
in action ; and in order that these pressures may exist, the 
jacket must be applied by shrinkage upon the tube. The 
pressure thus produced on the tube will strengthen it. 

It may be, however, that this pressure which is applied 
to the exterior of the tube will be so great that when 
the powder-pressure ceases to act it will compress the 
inner layer of the latter to such an extent as to cause this 
layer to pass its elastic limit. Thus the tube may be injured 
by the exterior force which is applied to strengthen it. 

It follows, therefore, that although the compound cyl- 
inder would support certain pressures in action if the req- 
uisite exterior pressure could be applied, it may be im- 
possible to apply this pressure to the exterior of the tube at 
rest, and therefore, before we can determine whether equa- 
tions (220), (221), and (222) represent allowable pressures in 
action, it is necessary to consider the effects of the pressure 
at rest upon the tube. 

When the powder-pressure acts, we have the forces P, 
at the interior and P 1 at the surface of contact of the cyl- 

These can be calculated by (220), (221), and (222). 

When the powder pressure ceases to act, the interior 
pressure becomes zero, and the variation of pressure at the 
interior is from -|- P to o. This difference between the 
pressure in action and at rest gives the variation of press- 
ure. Hence for the interior we have 

P. = ° - P., or /, = - P % (228) 

This is further evident by considering that the algebraic 
sum of the pressure in action and the variation of pressure 
must be the pressure at rest. 

GUNS. 211 

For the surface of contact of the two cylinders the 
pressure at rest is P/ and in action it is P t ; hence the varia- 
tion of pressure />, at that surface is, as before, 

A = P/-P, (229) 

117. Limiting Value of Exterior Pressure on Tube— System at 

The limiting value of the exterior pressure upon the 
tube for the state of rest is that value which will compress 
the inner layer of the tube to its elastic limit, and it is given 
by equation (209). 

P »=y^ZpP.> (23o) 

and no greater pressure than this can be allowed to exist at 
the exterior surface of the tube at rest. 

Now the pressure actually existing at this surface " at 
rest" is, from (229), 

P' = P*+P, (231) 

This value of P,' depends on P„ the pressure at the ex- 
terior of the tube "in action," and also upon/,, the variation 
of the pressure at that surface in passing from the state of 
action to that of rest. It is necessary therefore to calculate 
P/ by (231) and compare it with P s9 , the maximum admis- 
sible pressure calculated by (230). If P/ > P 1P , it. follows 
that it will strain the tube at rest beyond its elastic limit, 
and hence it cannot be allowed. The value P, p must then 
be adopted in place of P/ and be substituted for it in (231). 
This substitution in (231) will produce a corresponding 
change in the value of P,, and this change in P t will also 
change P a . (See equations (220), (221), (222).) On the other 
hand, if P,', from (231), be less than P i? from (230), P/ must 
be used and not P^ , because although the tube will support 
the pressure P lP > P,' at rest, if this value of P 1? be sub- 
stituted for P/ in (231) it will cause an increase in the value 
of P, , the pressure on the exterior in action. 

But it has been shown previously that the value of P x 
from equation (220) represents the greatest pressure which 
the jacket will endure in action without passing its elastic 


Hence this pressure must not be increased. 

We are therefore limited on the one hand to the value 
Ptf , equation (230), which must not be exceeded at rest, and 
on the other to the values P t and P lt equations (220), (221),. 
(222), in action which must not be increased. 

118. Calculation of/, in Equation (231). 

In order to calculate P/ from (231) we must know/,, 
since P t is given by (220). To calculate /, we proceed as 
follows : 

When variations of pressure occur at any surface they 
produce corresponding changes in the dimensions of the sur- 
face at which they act, and these changes depend directly 
upon the variations of pressure which cause them. The 
changes of dimensions in the direction of the circumference 
of the cylinder are the greatest (see equations (194) and 
(195) ), and hence it is only necessary to consider these. 

For the jacket, the exterior pressure is always zero, and 
the variation of pressure at the interior is/,. Equation (197) 
gives the change of the inner layer of a cylinder in the direc- 
tion of the circumference due to the forces P and P,. 

In the present case P t =/, , and P 1 — o. Also R,=R ir 
R — R lt £, = E„ hence 

X = <**-' + 2R ^ ( 232 ) 

l(R? - R?)E X ™ 2 > 

For the tube we have the variation of pressure /, acting 
upon the exterior surface, and /„ upon its interior. Equa- 
tion (212) gives the tangential change at the exterior of a 
cylinder due to the two forces P, and P,. To adapt it to 
the present case make 

P.=P.\ P,=P,- 
Making these substitutions, we have 

1 _ ae. > A-(4*. , + 2* 1 y 1 

1(R?-R:)E. • • • • Vll) 

Since the exterior surface of the tube and the interior 
surface of the jacket are in contact, they form virtually but 

GUNS. 213 

one surface, and whatever change occurs in one will occur 
also in the other. Hence the two values of A. in (232) and 
{233) are equal. 

Equating these and solving for/,, we have, since E a = E v 

Fl r;{r; - r?) {234) 

And since, from (228), 

we can find/, in terms of P a from 234. 

119. True Value of J> t . ' 

The true value of P is that which is safe for the system 
■both in action and at rest. 

It has been shown that if P/ < P lP , the values of P given 
by (221) and (222) are safe. 

If P/> P iP , these values are not safe and the true value 
of P„ is calculated as follows : 

The equation expressing the limiting value for the exte- 
rior pressure system at rest is 

^,P = -P,+A (235) 

in which the value of P IP is obtained from equation (230). 

^, = -P,p-A (236) 

Substituting the value of /, from (234), in which/, = — P , 

The equations expressing the limiting values of the in- 
terior pressure for the state of action are (221) and (222). 

Substituting the value of P x from (237) in (221) and (222) 
and taking the smaller value, we have the true value of P„ , 
which will be safe both in action and at rest, since it has 
been obtained by combining two equations which contain 
the conditions of safety both for action and for rest. 



The results of the substitution are , 

1 0« 




•w - 

R,° - 

2r;p h 




r ol> 

(4*,* - 

^r:) - 


(r; - 



of tube, 



Having the true value of P„ from (A) or (B), we find the 
true value of /, from (234), and this value of p 1 in (235), with 
the value of P i? from (230), will give the true value of P x . 

120. Calculation of the Shrinkage. 

Shrinkage is the difference of diameters of two adjacent 
cylinders. This is called the actual or absolute shrinkage. 
Dividing the absolute shrinkage by the diameter, we have 
the shrinkage per unit of diameter, or the relative shrinkage.. 

In Fig 83 let 

OA be the interior radius 
OB the exterior radius 
OC the interior radius 1 f ■ 1 
OD the exterior radius ( * ' 

before the cylinders are assembled. Then 

2BC = 2{OB - OC) 

is the absolute or actual shrinkage,, 

2BC _ 2{OB- OC) _ BC 
2OC ~ 2OC ~ OC 

is the relative shrinkage. 

When the cylinders are assembled, 
the surface of contact will take a po- 
sition such as E EE. The jacket will 
compress the exterior of the tube by 
the amount BE, and the interior of 
the jacket will be extended by the 
amount CE, and we have 

BE+ CE — BC, 

GUMS. 215 

By this compression the force P/ is exerted upon the 

exterior of the tube and the interior of the jacket. It is 

required to find BE and CE, and the shrinkage will then be 


Calculation. — The value -— - is the compression per 

unit of length of circumference, or of radius, of the exterior of 

the tube, produced by the force P/. This relative compres- 

sion is strictly— — -, since OB is the original exterior radius, 

but the error is so slight that it may be neglected. This 
compression is given by equation (213), since P = o, hence 

be { A r; + 2R?)p; 

OC - A ~ 3(R t '-R,')E.- • ■ ■ ■ VW 

The value -~r~ is the extension of the interior of the 

jacket per unit of length of circumference, or of radius, pro- 
duced by the force P/. 

It is given by equation (199) by making 

R, = R, ; />, = o ; 
R = R,; E, = E t ; 
P = P'. 


ce__ {ar: + 2* 1 yy 

OE~ 3(R,' -»- R?)E V ^ 239) 

The negative sign is omitted in (238),. since it simply indicates 

Hence denoting the relative shrinkage by cp, we have 

_ be + ce _ 2 r;(r,> - r:)p; 
(p ~ oc - eir: - r;)(r^ - r,j ■ { - 4 °> 

Steps. — The different steps in the calculation of the 
shrinkage may be thus summarized : 


i. Calculate P, e , >„» and P oP by (220), (221), and (222). 
Use smaller value of P . 

2. Calculate P lf from (230) and p, from (234), making in 
the latter p a = — P, , the value obtained from (221) and 

3. Find P( from (231), and compare this value with that 
of P 1P obtained from (230). 

If P s ' from (231) is greater than P 1P from (230), steps 4, 5, 
and 6 will be as follows : 

4. Calculate P ct and P af from A and B. Take smaller 

5. Recalculate /, from (234), making p a = — P t , the value 
found from A and B. 

6. Find P t from (237), using P lf from (230). 

7. Calculate the relative shrinkage by (240). The value 
of P,' to be used in (240) must correspond to the adopted 
value of P„ , being either (P, -\- />,) from (231) or P iP from (230) 
according as P is retained as originally found in step 1 or 
is changed as indicated in steps 3 and 4. 

8. The absolute shrinkage is obtained by multiplying 
the relative shrinkage by the interior diameter of the jacket. 
Hence if S denote the absolute shrinkage, 

5 = X 2R,. 

9. The exterior diameter of the tube should then be 

zR; = 2R^ + S. (241) 

121. Measurements in Gun-construction — Thickness of Wall — 
Length of Bore. 

Measurements. — The value of the shrinkage having 
been calculated by (240), the exterior diameter of the tube is 
given by (241). The exterior of the tube is then turned to 
this diameter, an error of 0.003 mcn only being allowed. 

After turning, the exterior diameters are measured at 
every inch of length of tube ; if too large, they are reduced ; 
if too small, they cannot be corrected, except by using a 
smaller jacket. Hence it is important not to turn below 

GUNS. 217 

The interior diameters of the tube are also measured at 
each inch of length. 

The tube and jacket are now assembled, and, when cool, 
the interior diameters of the tube under the jacket are 
again measured. 

The pressure of the jacket upon the tube will produce 
a contraction of the bore of the latter, and this contraction 
is given by equation (207), making P l = />/, since this latter 
is the pressure at rest. The measured contraction should 
agree with the calculated value ; and if it does, we have a 
proof of the accuracy of the measurements, and of the cor- 
rectness of the formulas. 

The agreement is generally very close. 

Thickness of Walls. — From previous calculations it 
has been shown that there is very little gain in tangential 
resistance by increasing the thickness of the cylinder beyond 
one calibre. This rule is generally followed in modern guns 
for the thickness of wall over the powder-chamber. 

The thickness at other points along the chase is obtained 
by a consideration of the powder-pressures at the different 
points, and these are given by the pressure-curve, whose 
construction has been explained. It is also necessary to so 
adjust the thickness of the different parts, that the weight of 
the gun shall not exceed the limit generally allowed for the 
different calibres, and that the axis of the trunnions or the 
centre of gravity of the gun shall be at "a distance from the 
breech, equal to about f the total length of the gun. 

The weights of guns are as follows, nearly : 

8-inch 14 tons 

10-inch 28 " 

12-inch 52 " 

12-inch mortar 13 " 

In general, the shape of the chase conforms to that of 
the pressure curve, and the resistance at different sections 
along the gun is calculated so that at any section it shall 
always be greater than the powder-pressure by a certain 
coefficient or factor of safety. For the 12-inch gun the 
elastic resistance is about 24 tons per square inch, and the 


powder-pressure 16 tons, at the chamber, so that the factor 
of safety is ff- = 1.5. 

Length of Gun. — For a given calibre, charge of pow- 
der, weight of projectile, etc., we can calculate by Sarrau's 
formulas tne value of u for a required initial velocity V, and 
may so adjust the elements of loading that the maximum 
pressure shall be constant and equal to, say, 15 tons for this 
velocity. Generally modern guns are from 35 to 45 calibres 

122. Wire Guns. 

In the built-up gun it has been shown that when in ac- 
tion, the inner layers of the tube and jacket are strained to 
their elastic limits respectively. None of the other fibres 
are strained up to that limit, and hence the total strength of 
the metal is not utilized. If instead of two cylinders we have 
four, assembled with proper shrinkage, the total thickness 
of the gun being constant, it is evident that the inner layers 
of each of the four cylinders would be strained to their 
elastic limits and hence more of the total strength of the 
metal would be utilized. As the number of cjdinders in- 
creases, the strength utilized will be greater, till we finally 
approach the limit where the cylinders are infinitely thin, and 
the whole thickness of metal in each is strained to its limit. 

Practical reasons, however, prevent the carrying out of 
this method, because the longitudinal strength of the cylin- 
ders decreases with the thickness ; the expense of boring 
and turning the cylinders is great, and it would be impos- 
sible to bore and turn very thin cylinders accurately. 

For these reasons, it has been proposed to substitute wire, 
for the rings or hoops of the built-up gun. This wire is' 
wrapped round an inner tube with a certain tension, so that 
the tube is compressed initially as in the case of the built-up 
gun, and the wire extended. 

The advantages claimed for the wire gun are : 

1. The tension of the layers of wire can be so regulated 
that each wire will be strained to its elastic limit when the 
system is in action, and we approach the condition of in- 
finitely thin cylinders. 

GUNS. 219 

2. The wire being very small in section, any physical 
de-fects can be detected, and hence all the metal in the gun 
will be sound. 

3. A high elastic limit can be given to the wire, and 
hence it will have a greater tangential strength than a forged 
steel hoop. 

4. In order to utilize the high elastic limit of the wire, 
the tube may be compressed at rest beyond its elastic limit. 

The objections are : 

1. Compressing the inner layer of the tube beyond its 
elastic limit violates the fundamental principle of modern 
gun-construction ; and if this is not done, the wire gun can- 
not in general be stronger tangentially than the built-up 
gun, since the strength of the tube marks the limit of the 
strength of the system. 

2. The coils of wire have no longitudinal strength, and 
hence the longitudinal strain must be supported, as in the 
built-up gun, by a jacket, and the attachment of this jacket 
to the tube presents difficulties. 

3. The wire gun is not as stiff longitudinally as the built- 
up gun, since the wire does not support the tube so firmly 
as the hoops. This is a question of importance with modern 
long guns. 

123. Description of Wire Guns — Woodbridge — Crozier — Brown 

Woodbridge (Fig. 84). — This gun consists of an inner 
tube, t, wrapped with wire as shown. Over the rear part 
of the tube is a jacket, J, made of longitudinal steel bars of 
wedge-shaped cross-section. 

This jacket is wrapped with the wire w, under such 
tension as to strongly compress the inner tube at rest. 
The longitudinal thrust is transmitted to the jacket as fol- 
lows : The jacket is screwed to the tube in rear ; the trun- 
nion-hoop t' bears against a thin hoop h, and this against a 
collar c screwed to the jacket in front. Hence the pull 
of the breech block in rear is transmitted to the rear 
of the jacket, and the thrust of the trunnions to the front 
of it. 






The calibre of the gun is 10 inches. 

Crozier (Fig. 85). — In 
this gun the tube is com- 
pressed initially beyond its 
elastic limit by the wire. 

The principal features are : 

1. The wire on the chase 
is covered on the exterior by 
thin hoops, put on with very 
slight shrinkage, so as to give 
stiffness, and protect the wire. 

2. A jacket of cast iron or 
cast steel is used for cheap- 
ness, to carry the breech- 
block and support the longi- 
tudinal strain. It is put on 
with very little shrinkage, the 
tangential strength of the 
gun depending on the tube 
and wire alone. 

3. The jacket and tube 
are connected, and the mo- 
tion of either prevented, by 
a series of rings or steps, a, 
abutting against each other. 

Brown Segmental (Fig. 
86). — In this gun there is first, 
a small lining tube, a, which 
extends beyond the trun- 
nions. The metal of this 
tube has a high elastic limit, 
112,000 lbs. The main tube, 
b, is made of wedge-shaped 
steel bars, of about the 
same elastic limit. This 
outer tube is wrapped with 
wire, and compressed to such 
an extent that its interior 














"> i 












Fig. 84. 

Fig. 85. 

is under compression even in action. This prevents the 

GUNS. 221 

joints between the bars from opening. The jacket is light, 
and is not in contact with the wire except at the trunnions 
and breech. The figure shows the method of attachment of 


A Fig. 86. A A. 

the breech-block. The pull of the block at the breech and 
the thrust of the trunnions in front are borne by the jacket. 

Relative motion of tube and jacket is prevented by the 
connection in rear. 

These guns have been made and tried in this country. 
In Europe the systems of Schultz, Longridge, Armstrong, 
and others have been tried. 


124. Necessity for — Measurements Required — Standard Comparator. 

NECESSITY for. — In a modern gun it has been shown 
that the stresses and shrinkages are functions of each other. 
Hence, if the correct shrinkage be not given to the gun, it 
will not properly support the stress to which it is subjected, 
and may be either strained beyond its elastic limit, or not 
strained up to that limit according to the actual value of the 
shrinkage as given in construction. After these shrinkages 
are calculated theoretically, their application to a particular 
gun, depends on the accuracy of the measurements made by 
the inspector during construction. Hence the necessity for 
accurate measuring instruments, and skill in their use. 

Measurements Required. — In general the following 
measurements are required in gun-manufacture : 

i. Interior diameters ; 

2. Exterior diameters ; 

3. Lengths; 

4. Measurements by templets and gauges. 
Standard Comparator. — In this case, as in all others 

where accuracy is required, all measurements must be re- 
ferred to a common standard. This standard is called a 



" comparator," and its general principles may be explained 
as follows : 

A stiff bed or body, a, of cast iron, Fig. 87, rests upon 
three le veiling-screws with rounded points of support. 

Fig. 87. 

In this bed is a groove or recess, c, in which rests a 
standard bar or rod, <:', accurately graduated in inches and 
decimal parts of an inch. On top of the bed is the rib d, 
which forms the guide for the heads e, f, and g , which slide 
along it. These heads can be fixed by clamp-screws in any 
position along the bed. e is called the fixed head, /the 
sliding head, and g the auxiliary head, h h are two sockets 
which carry steel points, and these points can be adjusted 
lengthwise in the sockets, and clamped by the clamp-screws ; 
i is a microscope reading 0.0001 inch ; k, a tangent screw con- 
necting /"and g. 

Use. — The primary object of thjs instrument is to lay off 
exact lengths. To do this, the graduated bar being in its 
recess c, bring the ends of the steel points h h in contact. 
Then adjust the graduated bar and microscope, till the zero- 
line of the eyepiece of the microscope coincides with the 
zero of the graduated bar. Clamp the fixed head, e, and 
slide the sliding and auxiliary heads, till the microscope is 
over the nearest division of the graduated bar correspond- 
ing to the length to be measured. 

The auxiliary head g is then clamped, and the sliding 
head f moved by the tangent-screw k till the microscope 
reads the required part of the inch. The distance between 
the points h h will then be the length required. 

125. Measurement of Interior Diameters of Short Hoops— Meas- 
uring-points — Use. 
The interior diameters to be measured may be — 



i. Those of a comparatively short hoop ; 

2. Those of a long hoop or tube. 

In the first case, when the length of the hoop is such that 
all parts of it can be reached by hand, measuring points or 
rods are used. 

Measuring-points.— For diameters from two to ten 
inches, the points are made of steel, and consist of a fixed 
point, a (Fig. 88), and a micrometer-point, b. The fixed point 

Fig. 88. 

varies in length according to the diameter to be measured, 
there being a number of them. Each one is threaded at the 
end, c, and the micrometer-point screws on this thread by 
the corresponding thread, c' . The screw d of the microme- 
ter is accurately cut, so that one turn of the head e cor- 
responds to a certain decimal part of one inch, generally 
0.025. The circle /is then graduated to read 0.001 inch. 

For diameters beyond 10 inches, the heat of the hand is 
found to affect the measurements, as it causes considerable 
expansion in a long steel rod. The rod, also, if made suffi- 
ciently light to be readily handled, would lack stiffness. 
For these reasons the measuring-points for larger diameters 
are made as follows : a (Fig. 89) is a holder of wood, bored 

Fig. 89. 

out in the middle, b, for the reception of the fixed and mi- 
crometer points c and d. Metal ferrules, e and/, of the shape 
shown, are fitted to the ends of the holders, and are pro- 
vided with clamp-screws, g, to clamp the points c and d. 


These points are essentially the same as before, the only 
difference being that the lengths of the holders vary, and 
the same points c and d are fitted to different holders. 

Use. — Suppose a given diameter, say 12.50 inches, is to 
be measured. The standard comparator is first set to 12.50 
inches, as just explained. A holder of proper length is then 
selected, and the points c and d fixed in it. The end of the 
fixed point c has an adjustment by which, having set the 
micrometer-point at zero, the length of the whole rod can 
be altered till it is exactly 12.50 inches. The interior diam- 
eter of the hoop can now be measured, and the differences^ 
if any, in thousandths of an inch, read off on the micrometer- 
scale on the point d. There are also other methods of ad- 
justing the rod. 

126. Measurement of Interior Diameters of Long Tubes — The Star 
Gauge — Setting the Star Gauge. 
The Star Gauge. — In the case of long tubes, all parts 
of which are not readily accessible, some means must be 
adopted of making the measurements at a distance from 
the operator. The instrument used for this purpose is called 
a " star gauge." Its principal parts (Fig. 90) are a long hol- 

Fig. 90. 

low brass rod, a, called the staff, to which are attached the 
head, b, and the handle, c. 

The figure and description are intended to give only 
a general idea of the instrument, and are not accurate in 
details, as the instrument is too complicated to be fully 
described here. 

The head b has three or more sockets, d, which are 
pressed inward upon the cone g by spiral springs, not 
shown in the figure. Into these sockets are screwed the 

GUN'S. 225 

star-gauge points e. There are generally three of these, 
120 apart, varying in length, for the different calibres to be 
measured, so that by screwing the proper points into the 
sockets d, any diameter can be measured. The handle c is 
at the other extremity of the staff a. In the older forms of 
star gauge it had a sliding motion along the staff. With 
the new instruments motion is given by a micrometer- 
screw. Extending through the staff is a square steel rod, /, 
united at one end to the handle c, and terminating at the 
other end in a cone, g. This cone has a known taper, and a 
forward movement of one inch corresponds to a certain 
definite increase in its diameter. This increase is marked 
on a scale upon the handle. 

Use. — When the handle c is pushed forward, the cone g 
also moves the same amount, since it is connected with the 
handle by the steel rod/. When the cone moves forward,, 
it pushes out the sockets d, resting upon its surface, and 
this forward motion of the handle and cone continues, till 
the points e come in contact with the walls of the bore to 
be measured. The amount of this outward movement of 
the points can then be read on the scale on the handle, and 
by comparing this with the original position of the points 
the size of the bore becomes known. 

Setting the Star Gauge. — As with the measuring- 
points previously described, it is necessary to " set" the star 
gauge before use ; that is, to establish an origin or datum to 
which all measurements are referred. Suppose the bore to 
be measured is 10.00 inches in diameter. Accompanying the 
instrument is a series of rings very accurately bored to the 
different sizes likely to be required in practice. The 10.00- 
inch ring is selected, and the standard comparator set to 
that length, a measuring-point adjusted to it, and the ring 
then tested by this point to see if it is exactly 10.00 inches. 
If not, the error is noted and corrected for. The 10.00-inch 
points having been screwed into the sockets of the star 
gauge, the ring is held so that when the handle is moved 
forward, the points will all touch the ring. While the 
points are in this position, the handle is adjusted so that the 
reading is zero. 



The ring is then removed, the instrument inserted in the 
bore, and the readings of the scale taken for every inch of 
length of bore. These readings are added to, or subtracted 
from, the original diameter of the ring, according as they 
are greater or less than zero, and the results give the true 
diameter of the bore. 

127. Exterior Diameters— Calipers— Arm— Support— Action. 

The instruments used for measuring exterior diameters 
are called calipers. One form consists, Fig. 91, of the arm 
a, the measuring-points b, c, and the support d. 

Fig. 91. 

Arm. — The arm a is made of steel in a semicircular 
form, and as light as possible consistent with stiffness. The 
arm terminates in sockets, e, at each end, which are provided 
with clamp-screws e' . 

To increase the stiffness of the arm and protect it from 
variations of temperature in use, it is covered with wood, /. 

The measuring-points b, c pass through the sockets e in 
the arm, and are clamped in position by the clamp-screws e'. 
The point b is called the fixed point, as it does not change 
its position relatively to the arm when once clamped ; the 
point c is the measuring or micrometer point, and having been 

GUNS. 227 

clamped in the socket e, its extremity, c', is capable of a 
small motion by means of a micrometer-screw, whose con- 
struction has been previously explained. This point carries 
a scale, s, reading to thousandths. The points when in posi- 
tion are always in a straight line. 

The arm with its points is suspended from its support, d, 
by the hook g and spiral spring h. 

Support. — The support of the calipers consists of a 
standard, k, fixed to a bar, /. This bar slides longitudinally 
upon a base, m. The standard k carries a rod, «, to which 
the spiral spring h is attached, and to this spring the hook^-. 
The whole support rests on the exterior of the tube to be 
measured, being brought parallel to the axis by the feet 00, 
and held in this position by the leather strap /, which is 
buckled tightly around the tube. 

Action. — Suppose a diameter of 15.00 inches is to be 
measured. Set the standard comparator to this length, and 
having determined from it the length of. a measuring-point 
of exactly 15.00 inches, set the micrometer-point c at zero, 
and adjust the points b and c in the sockets till the distance 
between them is exactly 15.00 inches. Raise or lower the 
caliper-arm till the points b and c are slightly above a hori- 
zontal plane through the axis of the tube. The bar / may 
then be moved along the tube parallel to its axis, sliding on 
the bed in, and measurements made for every inch of length. 
The bar / will slide for a length of 12 inches. The leather 
strap p must then be loosened, the whole support moved 
forward this distance, and the strap again tightened, when 
measurements may be made as before, till the whole is com- 

128. Measurement of Lengths — Step Gauge— Surface Lengths. 

The accurate measurement of lengths is very difficult to 
make, and as each particular case requires a special arrange- 
ment, only general ideas can be given. 

Step Gauge. — One of the most frequent measurements 
required is the length of the recess or step, ab, in a hoop. If 
this be too short, the hoop will not come in contact with the 
preceding one when shrunk on ; and if too long, an opening 




■^ a- — 

.i -e hoop. 



Fig. 92. 

will be left at the shoulder, which leaves the tube unsup- 
ported. To measure this length, an instrument called a step 

gauge is used. This con- 
sists, Fig. 92, of a steel blade. 
c, sliding through a socket 
in a body, ^. These blades 
are of different lengths, cor- 
responding to the different 
hoops to be measured. On 
the end of the blade is fixed 
a steel templet, f, which ex- 
actly fits the shoulder in the 
hoop. The templet being 
held against the shoulder b, while the body is pressed against 
the face of the hoop at e, the length can be read off on the 

Surface Lengths.— In each shrinkage operation, the 
changes in diameter and length due to that operation are 
measured. The changes in diameter are measured with the 
points, star gauge, or calipers. 

For measuring the changes in length, the following plan 
is adopted : 

Two holes are made with a punch in the exterior surface 
of the tube or hoop, and their exact distance apart before 
shrinkage measured as follows : 

An instrument, Fig. 93, consisting of a main body,«, car- 




6-CT '*? 




..... . .,. .( 


Fig. 93. 

ries a fixed head, b, and two movable points, c and d. The 
point c is attached to a sliding head, c', which carries a 
micrometer-screw, e. 

g is an extension-bar, having holes at intervals of 0.25 

GUNS. 220 

Accompanying the instrument are reference-bars,/, which 
have holes in them exactly one inch apart, and at the left 
end one inch is graduated into £, i, f inch. 

When the holes are punched in the surface of the hoop 
as before explained, their distance apart is measured 
approximately with a scale. Suppose this distance to be 
18.40 inches. 

Move the point d along the extension-bar g till it will 
enter the 18-inch hole, and clamp it, the screw d' passing 
into one of the holes in the bar^-. Place the instrument on 
the reference-bar/, the point centering the £-inch hole in it, 
and the point d resting in the 18-inch hole. The distance 
between the points c and <^is now 18.50 inches. 

Fix the micrometer e at zero, and move the points b and 
e till they are in contact. Now place the instrument on the 
hoop to be measured, the point c in one punch-mark and d 
in the other, make contact again with e, and subtract the 
reading of the micrometer-scale from 18.50 for the distance 
apart of the holes. 

After shrinkage the same process gives the distance 
apart of the punch-marks; and the difference before and 
after, the change due to shrinkage. 

129. General Principles of Measurements — Touch — Interior Diam- 
eters of Short Hoops. 

In the above descriptions all the complicated details of 
the instruments have been omitted, and only the general 
method of their operation and use given. The templet 
measurements require no special notice. A few general 
principles relating to the method of using these instruments 
must be understood. 

Touch. — The accuracy of all measurements with these 
instruments depends upon the skill of the operator, and 
hence practice is necessary to obtain satisfactory results. 
In most cases the sense of touch is relied upon to determine 
when proper contact of the measuring-points with the sur- 
face to be measured, is obtained. 

Various mechanical devices, such as electrical indicators, 
etc., have been tried to determine when proper contact has 



been obtained, and can be used to advantage when a large 
amount of measuring is to be done. 

Interior Diameters. — In measuring these (Figs. 94 


f if? ^ 










Fig. 94. 

Fig. 95. 

and 95), the hoop is placed horizontally, and the lower fixed 
point of the measuring-rod a is held by the operator at the 
point whose diameter is to be measured. It is evident from 
Fig. 95 that the diameter is the shortest line from a to b, and 
hence if the upper point of the measuring-rod be moved 
from b in the direction of the arrows, it will cease to touch 
the surface of the hoop. 

From Fig. 94, the diameter ab is the longest line in the 
cross-section ; and if the point be moved to either side of b, 
it will jam against the surface of the hoop. Hence in 
determining an interior diameter at any point with the 
measuring-rods, hold the fixed point of the rod firmly against 
the lower surface of the hoop at the point where the diam- 
eter is required. Move the micrometer-point in two direc- 
tions at right angles to each other, one along the axis of the 
hoop, the other across the axis, till a point is found where 
contact occurs due to both these motions. 

The reading of the rod will give the diameter. 

130. Interior Diameters of Long Hoops — Exterior Diameters — 
Vernier Scale. 

Interior Diameters of Long Hoops. — These are meas- 
ured with the star gauge^and in order that they may be 
correct the points must move at right angles to the axis of 
the bore. 

By the construction of the instrument these points must 
move at right angles to the staff of the star gauge, and hence 



it becomes necessary that the staff be placed accurately in 
the axis of the bore. For this purpose the gun or tube is 
carefully levelled, and various supports are used in the bore, 
which insure centering of the star-gauge staff. Exterior 
rests are also provided to support that part of the staff out- 
side the bore. 

Exterior Diameters. — In the measurement of exterior 
diameters, the same principles apply as to interior diameters. 
In Fig. 96 the diameter c is the longest line in the cross- 

Fig. 96. 

section, and the shortest line in the longitudinal section, 
Fig. 97. Hence the fixed point of the calipers is held at a, 
and the measuring-point b moved in two directions at right 
angles, as in case of the interior diameters, till proper con- 
tact is made. 

Vernier Scale.— *A very useful instrument in these 

Fig. 98. 

measurements is a "vernier scale," Fig. 98, which consists of 
a steel blade, a, graduated in inches and decimal divisions, a 


fixed jaw, b, a movable jaw, c, and an auxiliary jaw, d, with 
its tangent screw, e. The principle is the same as that of the 
standard comparator, lengths being measured between b 
and c. The advantage of this instrument is that it can be 
carried to any part of the shops, and when its error is 
determined by the standard comparator, it can be used in 
place of the latter with great convenience. Its disadvantage 
is that it is affected by changes of temperature when carried 
to different places in the shop, and when handled. 

1. In U. S. Service. 

131. Classification — Hotchkiss Mountain Rifle. 

Classification. — Cannon may be classified according 
to the service for which they are intended, into mountain, 
field, siege, or sea-coast guns ; according to the kind of fire 
they deliver, into guns, howitzers, and mortars ; according to 
the kinds of projectiles used, into smooth-bore and rifled ; 
and according to the methods of loading, into muzzle- and 
breech-loaders. As all modern guns are breech-loading 
rifles, it is most convenient for discussion to consider them 
according to the service for which they are intended. 

Machine and rapid-fire guns will be considered later. 


Hotchkiss Mountain Rifle. — This is the only gun of 
this class in service. It is made as light as practicable, so 
that it can be carried on the back of a mule, its weight being 
1 16 lbs. Its carriage weighs 220 lbs., and two men can pack, 
unpack, and mount it. 

The gun, Fig. 99, is made of steel in a single forging, the 

Fig. 99. 

trunnion-hoop being screwed on. The calibre is 1.65 
inches ; weight of shell loaded 2 lbs. 10 ozs.; of powder- 
charge, 5£ ozs. The initial velocity is 1275 ft.-secs. 



Breech Mechanism. — The mechanism is a simple form of 
the Krupp. It consists of a rectangular steel block, b, Fig. 

Fig. 100. 

100, with rounded corners ; its front face being at right 
angles to the axis of the bore, and its rear face slightly in- 
clined to that axis. 

This block slides transversely in a recess in the breech, 
and when withdrawn leaves the breech open for loading. 
It is locked in the firing position by a cam, c, entering a 
corresponding recess in the breech, and this cam is operated, 
and the block withdrawn and pushed home, by the lever- 
handle, /. e is the extractor for withdrawing the empty 
cartridge-case. It is a prismatic bolt, sliding in a groove in 
the upper part of the breech, parallel to the axis of the bore, 
and terminating in front in a hook, //. A tenon, i, on the 
under side of the extractor, fits in the extractor-groove, k, 
cut in the top of the breech-block. This groove is straight 
for some distance, and then curves quickly to the rear. 
When the block is withdrawn it moves in guides which are 
parallel to its rear face, and which consequently give it a 
motion such that the extractor is at first gradually with- 
drawn, thus removing the empty case from its seat in the 

The tenon of the extractor then enters the inclined part, 
a, of the groove in the block, and the extractor, with the 


cartridge-case, is drawn quickly backwards, thus ejecting 
the case to the rear. The motion of the breech-block is ar- 
rested by a stop-bolt, s, which is screwed through the upper 
part of the breech, and enters the groove r on the top of 

the block. 

Ammunition. — The ammunition is contained in a metallic 

cartridge-case, and as this forms a gas-check, no accurate fit 
of the parts of the mechanism is required, 
and the breech-block works freely in its 

II slot 
: t f~f^ ^p The charge is fired with an ordinary 

—.. ' ^r- > f r ; ct i on primer. The head of the case 
is formed by a cup, c, inside, Fig. 101, 
having five holes, a, in it. The exterior 
is strengthened by a cup, b, having five 
holes corresponding to a and a sheet- 
iron disk, d, riveted to the cups and case, 
and having a central hole, v. The flame 
from the primer passes through the hole 
v, and thence through a to the charge. 
The gas-pressure from the charge forces the cups b and c 
backwards, closing the hole v in d, and preventing the escape 
of gas. The projectiles are shell and canister. In order to 
use shrapnel, a heavier gun of 3-inch calibre has lately been 
adopted, weight 218 lbs. 


132. U. S. Field Artillery— 3.6-inch. B. L. Mortar— 3. 2-inch B. L. 
Field Gun, Light— 3. 6-inch B. L. Field Gun, Heavy. 

The field artillery in the U. S. service consists of the 3.6- 
inch mortar, 3.2-inch light field gun, and 3.6-inch heavy field 

Common Features. — See Figs. 102, 103, and 104. These 
pieces are all built of gun-steel ; are breech-loaders, and have 
rifled bores. They have conical gas-check seats, c, and cyl- 
indrical powder-chambers, d, of larger diameter than the 
bore, and these chambers are connected with the bore by a 
conical slope, e, forming the seat for the rotating band of 
the projectile, and by which it is centered in the bore. 

GUMS. 235 

In front of this powder-chamber slope is a second conica,. 
slope, /, which is formed by cutting away the tops of the 
lands of the rifling to a certain depth at the origin or begin- 
ning of the rifling, and gradually decreasing the depth of 
this cut to zero, at a certain distance from the origin, this 
distance varying with the size of the piece. As a rule one 
half of the lands are cut away at the origin. Thus for the 
3.6-inch gun the depth of the rifling groove is 0.04 inch, 
and the lands are cut away 0.02 inch at the origin. The ob- 
ject of this rifling slope is to allow the band of the project- 
ile to enter gradually to its full depth into the groove, and 
thus diminish the strain due to forcing. It also facilitates 
the loading of the projectiles,, and tends to prevent the 
escape of gas over the band, as the latter is forced readily 
and quickly to the bottom of the groove. 

3.6-INCH Mortar. — This is a short piece intended for 
vertical fire against troops pro- 
tected by intrenchments or irreg- 
ularities of ground from the direct 
fire of the field guns. 

It is made of a single piece of 
steel (Fig. 102), and is designed to FlG - I02 - 

use the same kind of powder and the same projectile as the 
3.6-inch field gun. 

It is mounted upon a cast-steel carriage, and the weight 
of piece and carriage are so adjusted that they can be read- 
ily moved by hand. 

3.2 and 3.6-iNCH Field Guns. — The 3.2-inch gun (Fig. 
103) is intended for use as a horse-artillery gun for rapid 
movements, and the 3.6-inch (Fig. 104) for the light or field 

Common Features. — The two guns are exactly similar in 
construction, and each consists of an interior tube, and a 
jacket, assembled by shrinkage. 

The tube is inserted in the jacket from the front ; a 
shoulder, a, on the tube resting against a corresponding one 
on the jacket. 

Forward movement of the tube in the jacket is prevented 
by the shoulder b, as shown in Figs. 103 and 104. The 

J u 1 

pL_ " 1 

riwr| e | d u £ | 








threads for the breech-block are cut in the rear end of the 

jacket, which thus supports the 
longitudinal stress. 

The principal dimensions, 
etc., are given in the table page 
253, with those of the siege 
guns, and of these, the weight 
of piece, charge, and projectile 
should be remembered. 

133. Breech Mechanism of Field 
Artillery — Principal Parts 
—The Breech-block. 

Principal Parts. — The 
breech mechanism comprises 
those parts which are neces- 
sary to open, close, and lock 
the breech, to prevent the 
escape of gas in firing, and 
through which ihe charge is 

The principal parts are : 

1. The breech-block, which 
closes the breech and, by its 
bearing on the fixed parts of 
the gun, supports the gas-pres- 
sure when the charge is fired. 

2. The obturator, which 
prevents the escape of gas. 

3. The carrier-ring, which 
guides the block as it is with- 
drawn from the breech, sup- 
ports its weight when with- 
drawn, and by which it is 
swung round, out of the way, 
for loading. 

4. The lever-handle or other 
device by which the block is 

rotated after firing, and its threads or bearings disengaged 
from those in the breech of the gun. 

! \ 




Fig. 104. 



5. The vent, by which fire is communicated to the charge; 
and the vent-closer, by which premature discharge is pre- 

The Breech-block. — In all guns in the U. S. service, 
except the Hotchkiss mountain-gun already described, the 
breech-block belongs to the French or interrupted-screw 
system. That is, screw-threads are cut around the exterior 
cylindrical surface of the block, and around the correspond- 
ing interior cylindrical surface of the breech-recess. To 
avoid the delay in unscrewing the block and screwing it 
home after and before each discharge, the circumferences of 
the block and breech-recess are divided in the field-guns into 
six equal sectors, and the screw-threads on every alternate 

Fig. 105. 

sector removed, thus leaving on the block, and in the breech- 
recess, three threaded and three slotted sectors of equal 
width. By this arrangement the block can be pushed in or 
pulled out of its recess, the threaded sectors on the block 
sliding in the slotted sectors of the breech-recess. After it 
is pushed home to within one sixth of a turn of the thread, 
or one sixth of the pitch, a rotation through an angle of 
6o° will cause the threads on the block to engage in those 
in the jacket, and the threads thus engaged are found to 
have ample strength to resist the pressure of the powder- 
gas. The threaded and slotted sectors of the block are 
partly shown in Fig. 105. The exterior diameter of the 
block at the threaded portion, is greater than that of the 


powder-chamber, in order to give as large a surface as possi- 
ble for the screw-threads and thus increase their relative 
strength, and also to leave a large opening in the breech to 
facilitate the insertion of the projectile and charge. The 
length of the block is greater than its exterior diameter, to 
give a greater number of threads, and thus distribute the 
pressure of the powder-gas over a greater number of them, 
and reduce the stress on each, and consequently the ten- 
dency to strip. The front face of the block is plane, and the 
rear face has certain projections whose uses will be explained. 
The diameter of the unthreaded portion in front is less than 
that of the threaded portion, in order that it may enter for 
a short distance into the gas-check seat in the rear end of 
the tube. The rear end is not threaded, and has a shoulder, 
a, uponit, which fits tightly against the rear face of the car- 
rier-ring when the breech is closed, and thus prevents the 
entrance of dust in transportation. The interior is bored 
out for the reception of the parts of the obturator, and cer- 
tain grooves are made on the exterior whose object will be 

134. The De Bange Obturator — Action — Remarks. 

The obturator prevents the escape of gas around the 
threads of the breech-block and through the mechanism. 
Two obturators are used in the field service : the De Bange, 
with the 3.2 and 3.6 rifles, and the Freyre, with the 3.6 

The De Bange Obturator.— This consists (Fig. 106) of 
a central spindle or stem, a, terminating in front in a large 
head, b, called, from its shape, the " mushroom-head "; the 
vent, c, with a copper bushing, d, in front, and the primer- 
seat, e, in rear ; two steel cups, //', called gas-check cups, 
and between them a plastic pad, g, made of asbestos and 
tallow, strongly compressed by hydraulic pressure before 
its insertion, and covered with canvas, the outer edges of 
the pad being protected by two thin strips of copper, m\ an 
obturator-nut, h, held in place by a spline-screw, k, which is 
halved into the nut and spindle ; and a spiral spring,/, bear- 



ing against a shoulder in the breech-block, and against the 
front of the obturator-nut, h. 

When in place in the gun, the spindle a passes through 
the axis of the breech-block, the outer surface of the pad g 

Fig. 106. 

rests against the gas-check seat in the gun, and is held be- 
tween the elastic gas-check cups//'. The mushroom-head 
b is in the powder-chamber. 

Action of the De Bange Obturator. — When the 
charge is fired, the gas-pressure acts normal to the surface 
of the mushroom-head, and the latter, with its spindle a, is 
forced to the rear. The pressure is thus transmitted to the 
gas-check cups //', and the elastic pad g, being held by 
the front of the block and pressed between the cups //', is 
forced to expand radially and pressed firmly against the 
walls of the gas-check seat, preventing the escape of gas. 
An elastic packing-ring, n, also expands under the pressure, 
and, fitting tightly against the spindle a, prevents the flow 
of the tallow of the pad, and thus avoids the sticking of the 
pad to the spindle. When # the pressure is removed, the 
action of the spring / keeps all the parts, cups and pad, in 

The pad has the shape shown in order to have as small 
a surface as possible in contact with the spindle and the 
Avails of the gas-check seat, to avoid sticking, and to furnish 



in the middle a reservoir of material that may be pressed 
outward and inward and thus secure perfect contact. 

Remarks. — The canvas cover of the pad prevents its 
breaking in use. The shape of the gas-check cups is such 
as to avoid all sharp angles which would cut the pad, and 
to retain the edges of the cups for preventing the flow of 
the tallow. The elastic packing-ring n also assists to pre- 
vent this flow. The spline-screw k prevents the unscrewing 
of the obturator-nut k, which is liable to occur when the 
breech-block is rotated for withdrawing, owing to the stick- 
ing of the pad to the walls of the gas-check seat. 

135. The Freyre Obturator — Action — Remarks. 

The Freyre Obturator. — This obturator (Fig. 107) is 
used with the 3.6-inch mortar, and consists of a central spin- 


Fig. 107. 

die, a, terminating in front in a large flat disk ; the vent b and 
its copper bushing, c, in front, and the primer-seat in rear ; 
the threads and nuts, dd', the rear nut, d', being a locking- 
nut with a left-hand thread, wlyle the obturator-nut, d, has a 
right-hand one, and hence d' prevents d from unscrewing 
during the rotation of the block ; the spiral spring e, bear- 
ing on a shoulder on the spindle a and a corresponding 
shoulder in the block, and tending to push the spindle con- 
stantly forward ; and the gas-check ring /. The exterior 
surface,^ - , of the head of the spindle is conical, and ground 

GUNS. 241 

to an exact fit with the interior surface of the conical gas- 
check ring, /. This ring / is made of steel of high elastic 
limit, and when in place, rests against the front face of the 
breech-block as shown, and its length parallel to the axis of 
the bore is such that when in this position there is a space, 
h, between the head of the spindle and the front face of the 
breech-block. When in place, the spindle a passes through 
the axis of the breech-block, the outer surface of the elastic 
gas-check ring / rests against the walls of the gas-check 
seat, and the front surface of the spindle-head is in the 

Action of the Freyre Obturator. — When the charge 
is fired, the gas, acting normal to the spindle-head, presses it 
backward into the conical ring /, the space h allowing this 
movement. The ring, /, being held against the face of the 
breech-block, is thus forced to expand radially by the wedg- 
ing action of the spindle-head, and is pressed firmly against 
the walls of the gas-check seat, preventing the escape of gas 
around the exterior of the ring. The tight fit of the two 
conical surfaces prevents any escape between the ring and 
head. When the pressure of the gas is removed, the elas- 
ticity of the ring /and the action of the spring e return the 
spindle-head and ring to their former positions. 

Remarks. — This obturator has the following advan- 
tages : 

1. Being of metal, it is very slightly affected by changes 
of temperature, weather, etc. 

2. It occupies very little space in the powder-chamber; 
and hence when space and consequently weight are impor- 
tant, as with this mortar, it is used. 

Its disadvantage is that it is liable to get out of order. 
A blow struck on the thin edge of the ring / in loading, or 
closing the breech, would allow the gas to escape; and 
after a channel is once formed for the gas, the obturator 
is useless. This accident is liable to occur in field service, 
and to guard against it to some extent the spindle-head is 
made to project well beyond the front edge of the ring. 
This projecting portion would ordinarily receive any blow 
which might injure the edge of the ring/. 



It will be observed that the spiral spring j in the De 
Bange obturator, Fig. 106, acts in the opposite direction to 
that of the Freyre, Fig. 107. The reason is as follows: The 
gas-check ring in the Freyre being elastic, when proper 
compression of this ring is once secured by the nuts dd', it 
will be retained unchanged. With the De Bange the pad is 
not elastic, and hence if properly compressed before firing 
this compression will change after firing, due to the great 
pressure upon it. Hence a constant tension is always re- 
quired with the De Bange to keep the cups and pad in 
place, while with the Freyre the spring is used to push the 
spindle forward, and assist in restoring the ring to its for- 
mer position. 

136. Carrier-ring — Object of Latch. 

Carrier-ring. — This ring guides the block, supports 
its weight when it is withdrawn from the breech, and en- 
ables it to be swung round to one side of the gun, out of the 
way of loading. It consists (Fig. 108) of a ring of steel, h, 

\\-C .■ 

^^ "*v 




> 1 
1 1 

\e j 

• 1 

,a- Hv : 

Fig. 108. 


1 J 
I / 
1 1 
ji L 



. ! 1 


which surrounds the breech-block, and through which the 
breech-block slides parallel to the axis of the piece. The 
breech-block occupies the space a. On the interior there 
are three lugs, b, the exact width of the slotted sectors of 

GUNS. 243 

the block. These lugs bear in the slotted sectors, and fur- 
nish guides for the block when it is drawn to the rear, so 
that it is compelled to move parallel to the axis of the gun. 

On the left-hand side is a stop, c, which travels in a 
groove in the breech-block, and limits the motion of transla- 
tion of the latter when it is withdrawn from the breech, and 
also its motion of rotation, when turned to lock into the 
threads of the breech of the gun, or unlocked for withdrawal. 
This stop passes through the carrier-ring and is secured by 
a screw, d. The stop may occupy any other convenient po- 
sition, and may be a simple stud, as in the case of the mor- 
tar, where the stop is at the top of the carrier-ring. 

Two lugs, e e, are for the purpose of attaching the carrier- 
ring to the jacket, by a pin which passes through holes in 
the lugs, and corresponding holes in the jacket. This pin 
forms the axis around which the carrier-ring, with the block, 
swings, when the breech is open for loading. The exterior 
surface, g, of the carrier-ring is conical, to secure a good fit 
in the breech. 

Object of Latch. — When the threads of the breech- 
block are disengaged from the corresponding threads in the 
breech, the block is pulled to the rear through the carrier- 
ring. It is evident, however, that this pull upon the block 
will cause the carrier-ring to swing around the pin passing 
through the lugs e, and this will tend to jam the block, and 
prevent its movement to the rear. To avoid this, the car- 
rier-ring must be locked to the gun while the block is mov- 
ing to the rear. When the travel of the block is finished, 
the carrier-ring must be unlocked from the gun, in order 
that it may be swung round with the block to the loading 
position. These objects are accomplished by the latch /, 
shown in Fig. 108 and in detail in Fig. 109. 

137. Description of Latch and its Working. 

The latch consists of a piece of metal shaped as shown in 
Fig. 109. The lower inner end, a, fits against one of the 
slotted sectors of the breech-block, and is constantly pressed 
down upon it by the action of the flat spiral spring b, acting 
on a shoulder, c, of the latch and a corresponding shoulder, 



d, of the latch-recess 




All the working parts are covered 
by the latch-plate i (see Fig. 108), 
secured to the exterior of the 
carrier-ring by two screws, J, so 
that in case any part breaks it may 
be readily removed and repaired. 
The front of the carrier-ring next 
the breech has a hole, g, cut through 
it, and opposite this is a recess, k, 
in the corresponding face of the 

Action of the Latch. — Suppose 

the breech closed and the gun 

end of the breech-block is a trans- 

Fig. 109. 

fired. At the rear 

verse groove, a, Fig. no, which is on a level with the slotted 

sector of the block at c, and gradually increases in depth to 






(1Y1YIY v 





Fig. 1 10. 

its end, b. The depth of this groove at b is such that when 
the inner end of the latch rests in it, the action of the flat 
spiral spring, b, Fig. 109, will force the latch down sufficiently 
far to release it from the jacket. The inner end of the latch 
rests at b during firing, and hence at this time the carrier- 
ring is unlocked from the jacket, and there is no strain on 
the latch. After firing, the first operation in opening the 
breech, is to rotate the block in the direction of the arrow. 
As the latch is in the carrier-ring, it does not rotate with the 
block, and hence the action of the groove a is to push up' 
the latch into its recess in the breech, and thus lock the car- 
rier-ring to the jacket. The inner end of the latch now 
stands at c. The block is now withdrawn, the inner end of 

GUNS. 245 

the latch sliding along the slotted sector, and keeping the 
carrier-ring locked to the jacket. This continues up to the 
point d. 

At this point, the path of the inner end of the latch be- 
gins to descend along a gradual slope from d to e. Hence 
by the action of the flat spiral spring, the latch begins to 
move out of the jacket, being forced inward into the groove 
de. At the end of the travel of the block, corresponding to 
the point e, the depth of the groove de becomes sufficient 
to allow the entire withdrawal of the latch from its recess 
in the jacket, and hence at this instant the carrier-ring 
becomes unlocked, and the block and ring can be swung 
round for loading. 

After Loading. — After loading, when the block and car- 
rier-ring are swung round to close the breech, the pressure 
of the hand is applied to the rear end of the block. This 
pressure would tend to move the block forward through 
the carrier-ring, and hence jam the ga^-check against the 
breech. The block must therefore be locked positively to 
the carrier-ring in the loading position, and this is done as 
follows : 

The extremity e of the groove a in the block, termi- 
nates in a cylindrical hole, into which the inner end of the 
latch drops at the end of its motion. The block therefore 
cannot move with reference to the carrier-ring, till the latch 
is lifted from this hole e. This is accomplished as fol- 
lows : 

There is a conical stud, s (see Fig. 109), projecting from 
the rear face of the base ring, which, as the carrier-ring is 
closed, passes through the hole g, Fig. 109, in the front face 
of the carrier-ring, and enters the recess h in the front of 
the latch. This stud, bearing against the inclined end of the 
recess h, owing to the shape of the two surfaces, raises the 
latch slightly till it clears the cylindrical hole e, Fig. no, 
and stands at such a height that when the block is pushed 
forward, the lowest part of the inclined surface de will pass 
under the inner end of the latch, and thus cause it to move 
up the inclined surface and push the latch home. 




Fig. hi. 

138. The Lever-handle. 

This is a device for rotating the breech-block. In the 
mortar there are two of these handles fixed to 
the block at opposite extremities of a diameter 
(Fig. in). 

In the 3.2 and 3.6-inch guns there is one 
handle, h, pivoted to the upper part of the 
block by a pin, e, Fig. 112. This handle is 
raised vertically for rotation ; and when low- 
ered for firing, its lower end fits into a recess, 
c, in the end of the jacket, for additional secur- 
ity against accidental opening. To limit the 
vertical motion of the handle when it is raised, 
a stop, a, is placed upon the pin e, which abuts 
against a corresponding stop, b, on the lug /. 
The head d of the lever-handle, is eccentric, 
and forms a cam, with the following objects: 
When the block is in the firing position, this 
cam d enters a corresponding recess, r, in the 
rear face of the carrier-ring, and thus locks the 
block to the ring, and with the end of the lever- 
handle, as before explained, prevents any rota- 
tion of the block in firing. When, after firing, the lever- 
handle is raised and the block rotated, if an attempt be made 

Fig. 112. 



to withdraw the latter, it sometimes fails on account of the 
sticking of the pad in its seat. If the lever-handle be now 
lowered, the surface of the cam d bears against the rear face 
of the carrier-ring, since no recess is cut for it in this posi- 
tion, and thus exerts a powerful leverage, sufficient to start 
the pad from its seat. 

The lever-handle is made to work tight between its lugs 
in the block, in order that it may not fly up from its recess 
in the carrier-ring, by the shock of discharge. 

In the 3.2 and 3.6 guns there is a fixed bronze handle, g, 
attached to the breech-block for the purpose of withdraw- 
ing it. 

139. The Vent-cover. 

This is a device to prevent the insertion of a primer, and 
the premature discharge of the piece, before the breech- 
block is locked. It must be so arranged that the vent will 
be closed at all times, except when the threads of the block 
are engaged in those of the breech. 

3.6 Mortar. — For the 3.6 mortar the device is as follows: 
A handle, a, Fig. 113, is attached to a shaft, b, which fits 

Fig. 113. 

into a recess on the left side of the breech-block. The 
shaft is shown in cross-section at c. When turned into the 



position shown in the figure, so that the vent is open, the 
corner d projects through the block, and binds against the 
edge of one of the lugs / in the carrier-ring, so that when 
in this position, with the vent uncovered, the breech-block 
cannot be rotated to open the breech. The piece e is 
attached to the shaft b, and closes the vent. When open or 
closed, its ends rest on two pins, f, which retain it in posi- 
tion, and its motion in opening or closing is limited by two 
studs, g. In order to rotate the breech-block, the vent must 
first be closed by turning the shaft b upwards by the handle 
a. The corner d of the shaft then no longer bears on the 
edge of the lug in the carrier-ring, and the surface h forms 
part of the exterior curved surface of the block. 

3.2 and 3.6 Guns. — For these guns a radial slot, a, Fig. 1 14, 

Fig. 114. 

is made in the rear part of the breech-block which projects 
outside the carrier-ring. In this slot slides a piece of metal, 
b, having a pin, c, projecting from its forward face next the 
breech of the gun. A groove, d, is cut in the rear face of 
the carrier-ring, which is eccentric at its lower end, and the 
pin c bears in this groove. 

When the block is pushed home, the pin enters the 
groove at e, and its weight keeps it over the vent, as it 
stands in a vertical position during the time the block is 
withdrawn. As the block is rotated to the right in closing, 
the vent is still covered, due to the bearing of the pin c in 
the concentric part of the groove d. At the last instant of 
rotation, however, the pin c enters the eccentric part of the 
groove d, the vent-closer is lifted, and the vent uncovered. 



140. Action of Mechanism of 3.6-inch Mortar. 

1. Suppose the breech closed and ready for firing. In 
this position, the threads of the block are engaged in those 
of the gun, the gas-check is in its seat, the vent-cover has 
been moved to the right, or downward, by hand, thus uncov- 
ering the vent. By this motion of the vent-closer, the corner 
of the shaft, as before explained, has been caused to project 
beyond the surface of the block, and to bind against the 
edge of one of the lugs of the carrier-ring, so that the block 
cannot be rotated while the vent is open. The inner end of 

the carrier-ring latch is in the extremity d of the transverse 
groove e, Fig. 115, the outer end has left its recess, g, in the 
gun, and the carrier-ring is unlocked from the jacket. 

2. After firing, the elasticity of the spiral spring and of 
the gas-check ring acts to move the ring from its seat in the 
gun, and restore it to its former position before firing. 

The vent-closer/ is now turned upward, closing the vent, 
and at the same time unlocking the block from the carrier- 
ring, so that it may be turned to the left by the handles a a. 
The block is then turned to the left 6o°. By this operation, 
the threaded sectors on the block come into the slotted 
sectors in the breech, so that the block can be pulled to the 


rear through the carrier-ring. While the rotation of the 
block is taking place, the inner end of the carrier-ring latch 
is moving up the inclined groove e, and the outer end of the 
latch has been pushed into the recess g in the jacket, thus 
locking the carrier-ring to the jacket. The block is now 
pulled to the rear through the carrier-ring till its motion is 
stopped by the stop b in the carrier-ring striking against the 
tront shoulder, b', of the longitudinal groove k. During this 
motion of the block the inner end of the carrier-ring latch 
is bearing on the surface of one of the slotted sectors, and 
the carrier-ring remains locked to the gun. Near the end of 
the motion of the block, however, the inner end of the latch 
begins to descend along an inclined groove, h, in the' surface 
of the block, and the outer end, due to the action of the flat 
spiral spring before described, is withdrawn from its recess, 
g, in the gun. At the end of the travel of the block, this with- 
drawal of the latch is complete, and the inner end of the 
latch drops into a cylindrical hole, i, at the end of the inclined 
groove, thus locking the block to the carrier-ring. The 
block and carrier-ring are now swung round by hand out of 
the way for loading. 

3. To close the breech the block and carrier-ring are 
swung round into place. As the carrier-ring closes against 
the breech, a conical stud, s, Fig. 109, on the rear face of the 
latter enters a recess in the front of the latch, and lifts the 
inner end of the latter out of the cylindrical hole i in the block. 
The block is now pushed forward by hand, sliding through 
the carrier-ring, the latch is pushed up into its recess in the 
jacket by the action of the inclined surface h on the block, 
and the forward motion of the block is continued till the 
rear end of the groove k strikes against the stop b. The 
block is then rotated to the right 6o°, engaging its threads 
in those of the breech. At the same time the inner end of 
the latch moves down the inclined transverse groove e, and 
the upper end of the latch is withdrawn from its recess g in 
the gun, thus unlocking the carrier-ring from the gun. The 
rotation of the block to the right is limited by the stop b 
striking against the shoulder b" at the end of the transverse 
groove j. The vent-closer is then turned down by hand, 





thus opening the vent and locking the block to the carrier- 
ring, and the mechanism is in its firing posi- 

The action of the mechanism of the 3.2 and 
3.6 field-guns is exactly similar, except that the 
vent-closer is automatic. 


141. 5-inch Gun— 7-inch Howitzer— 7-inch Mortar. 

Siege-guns are intended for attacking and 
defending permanent inland works, and the 
land fronts of sea-coast fortifications. 

In the U. S. service the pieces are : 
The 5-inch siege-gun ; 
The 7-inch howitzer; 
The 7-inch mortar. 

Common Features. — These guns, like the 
field-guns, are built of gun-steel, and are breech- 
loading with rifled bores. They have conical 
gas-check seats, and cylindrical powder-cham- 
bers of larger diameter than the bore, with 
which they are connected by a conical slope 
for centering the projectile. They have also 
the conical rifling slope or forcing-cone, formed 
as explained in the field-guns, and for the same 

5-inch Siege-gun. — This gun is intended 
for direct fire in siege operations. It is built 
up (Fig. 116) of a tube, jacket, trunnion-hoop, 
a, sleeve, b, locking-ring, c, key-ring, d, and 
base-ring, /. The tube is inserted into the 
jacket from the rear. The peculiarity of this 
gun is the manner of assembling the trunnion- 
hoop. It would be preferable to have the 
jacket and trunnion-hoop in one piece, as in 
the field-guns, but difficulties in making such 
a forging of the required physical qualities 
prevent this, and hence the jacket is extended 


under the trunnion-hoop to give better support to the tube, 



and the trunnion-hoop assembled over the front of jacket 
as shown. 

The surface of contact of jacket and trunnion-hoop is a 

cone, with the larger base to the front,and this tends to lock 

the trunnion-hoop in place, and prevent any forward motion. 

Relative motion of tube and jacket. is prevented by the 

shoulder e and base-ring f. The locking-ring 

c prevents forward movement of the sleeve 

b, which is important, as the trunnion-hoop 

abuts against b, and hence brings a thrust 

upon it when the piece is fired. 

7-inch Howitzer. — This is a compara- 
tively short, light piece, of large calibre, in- 
tended to carry a shell, with a large bursting 
charge, and to give a high-angle or curved 
fire, and reach troops sheltered by a parapet, 
and also to breach masonry protected by 
an earthen cover, to destroy earthworks, etc. 
It is built up of a tube, a jacket, a trun- 
nion-hoop, a sleeve, a locking-ring, a key-ring, 
and a base-ring, assembled by shrinkage (Fig. 
117). The construction is shown in the fig- 
ure. The tube is inserted into the jacket 
from the rear, and has a shoulder at e which 
prevents forward motion. The longitudinal 
stress is transmitted from the trunnions to 
the jacket through the locking-lip a, and for- 
ward motion of the sleeve b is prevented by 
the locking-ring c. The key-ring d is shrunk 
over the locking-ring. 

7-inch Mortar.— This is a short rifled 
piece intended to carry the same shell as the 
7-inch howitzer, and give a vertical fire. It 
is built of a single piece of forged gun-steel (Fig. 118), and 
resembles the 3.6-inch field-mortar. 

Breech Mechanism. — The breech mechanism of the 5-inch 
siege-gun and 7-inch howitzer, are similar to that of the 3*2- 
inch gun already described. The breech mechanism of the 
7-inch mortar differs from that of the 3.6 mortar in the fol- 
lowing particulars : 




Fig. 117. 



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i. It has the De Bange gas-check. 

2. The vent-closer is a sliding piece which is moved over 
the vent by turning a handle similar to that in the 3.60 
mortar. This turning of the handle to open 
the vent locks the breech-block to the carrier- 

The principal data relating to the field and 
siege artillery are given in the table on page 







Fig. 118. 

142. Calibres — Common Features — 8-inch Rifle. 

Calibres. — The guns at present adopted 
for the U. S. seacoast service are : 

8-inch ) 

10-inch \ steel B. L. rifles ; 

12-inch ) 

12-inch steel B. L. mortar; 

12-inch rifled mortar, with cast-iron body and 
steel hoops. 

Common Features. — The guns are intended for direct 
fire against armored ships; the mortars, for vertical fire 
against the decks of war-ships. The seacoast guns, with the 
exception of the 12-inch mortar with cast-iron bod) 7 , are 
built up of gun-steel, and are breech-loading with rifled 
bores. They have conical gas-check seats, cylindrical pow- 
der-chambers, which are connected with the bore proper by 
a conical slope, and they have also the rifling slope, called 
the forcing-cone, already described in the field and siege 

The 8-inch Gun, Fig. 1 19, is composed of a tube, T, in- 
serted into the jacket from the rear, a jacket, J, two C or 
chase hoops, one D hoop, four reinforce or A hoops (A, 
being the trunnion-hoop), and a base-ring, R. 

Relative motion of tube and jacket is prevented by the 
shoulder a and the base-ring. The other shoulders on the 
tube reduce its thickness by successive steps from rear to 
muzzle. C 1 and C, hoops are locked together by a locking- 
lip, g, as shown, Fig. 120, the smaller diameter of the lip, 
C t being expanded sufficient!)' by heat to pass over the 






larger diameter of C r This prevents relative motion of C, 
and C 2 hoops. The C hoops in all guns have a tendency 
to move forward, probably due to the vibration 
Sj_[ of the chase and other causes, and to prevent this, 
four pins, /, Fig. 121, pass through the C, hoop 
radially into the tube. The D hoop overlaps the 
joint between jacket and C l and by means of the 
shoulders at c and c', locks the C, hoop to the 
jacket, and hence the jacket and C, are not locked 
together by a lip. The small ring e is called a 
filling-ring. It is necessary, because in assembling 
ty)- jj ' the D hoop it is desirable to make a tight contact 
at the shoulders c and c' . The rear end of D is 
C4 therefore made of such length as when hot to fill 

the space from c' to jacket-shoulder. Hence when 
cold there will be an opening at b, which is filled 

Fig. 120. 

Fig. 121. 

by turning out a groove, and driving into it a split 
ring of metal, e. This gives stiffness to the chase. 
The trunnion or A^ hoop abuts against a shoulder 
on the jacket at d. The longitudinal strain due to 
firing is then distributed along the jacket from 
the base-ring to the shoulder d. 

The reinforce or A hoops are not locked, be- 
cause there is no tendency to slide in these hoops, 
and the reinforce does not require stiffening. 

As a rule, it may be observed that the locking 
of hoops together is for two purposes : 

1. To obtain longitudinal stiffness. 

2. To prevent sliding. 

Hence reinforce-hoops need no locking, and 
Fig. 119. chase-hoops are not locked when the joint be- 
tween them is overlapped by an exterior hoop. 



°? s 




143. The 10 and 12-inch Rifles. 

In these guns (Fig. 122) the tube is inserted into the 
jacket from the front, as in the field-guns, and the breech- 
screw threads are cut in the jacket. 

The parts of the 10 and 12-inch guns are : 

One tube ; 
One jacket ; 
Two C hoops ; 
One D hoop ; 
Three A hoops ; 
Three B hoops ; 
Four securing-pins,/"; 
One filling-ring, e. 

The following features of construction may 
be noted : There are relatively few pieces, and 
consequently the hoops are very long. This 
gives great longitudinal stiffness. The chase- 
hoops are locked together by a locking-lip, g, 
and the sliding of these hoops prevented by the 
four pins/". 

In the 10 and 12-inch guns there is no shoul- 
der in the jacket to prevent forward motion of 
the tube. This motion is therefore prevented 
by the bearing of the C, hoop against the shoul- 
der a on the tube, and the C, hoop is held in 
place by the D hoop locking over two shoul- 
ders, one on the jacket at c' , and the other on 
the C 1 hoop at c. 

The D hoop is shrunk on over these shoul- 
ders as shown in the figure, locking the jacket 
and C, hoop together ; and as tight joints must 
be made at c and c\ the length of the D hoop 
must be such as to exactly fill the space between 
b and the shoulder on the jacket at c' when hot. 
Hence when cold it will leave an open joint at 
b, and this is filled by turning out a groove and 
putting in the filling-ring e. It will be observed 
that this same construction is used in the 8-inch 



Ii ■ ■ 



Fig. 126. 

Fig. 123. 

Fig. 124. 

Fig. 125. 

Fig. 127. 



gun; but 





it is of greater importance here, as the C y hoop is 
on to hold the tube in place, while in the 8-inch 
gun a shoulder on the jacket does 
this. The A 3 hoop has a shoulder, 
m, near its rear end which fits over 
a corresponding shoulder on the 
jacket. By the shrinkage of the A, 
hoop on the jacket it has a firm hold 
on the latter, and hence this shoul- 
der on the jacket, bearing against 
the shoulder on A 3 , strengthens the 
jacket longitudinally, since it dis- 
tributes a portion of the pull of the 
breech-block to the A s hoop. The 
forward thrust of the trunnion-hoop 
B 1 is transmitted to the shoulder n 
on the A l hoop, and from the A y 
hoop to the jacket by the shoulder d. 
Thus the jacket takes the longitudi- 
nal strain in all cases. Figs. 123 to 
127 show the 8, 10, and 12-inch guns 
drawn to the same scale and giving 
their relative sizes, and also the 12- 
inch mortars, which are to be de- 

Fig. 128. 
gun, and 

^ £ 





144. 12-inch Steel Mortar — 12-inch Cast- 
iron Mortar, Steel-Cooped. 

12-iNCH Steel Mortar. — This 
mortar, Fig. 128, is composed of — 

One tube ; 
One jacket ; 
Two C hoops ; 
One D hoop ; 
Three A hoops ; 
One base-ring. 

The tube is inserted into the 
jacket from the rear, as in the 8-inch 

As the 

Fig. 129, 
the shoulder a prevents motion of tube. 

GUNS. 259 

piece is short, and therefore stiff, the C hoops are not locked, 
but four radial securing-pins are inserted in the muzzle-hoop 
to prevent sliding. 

12-inch Mortar with Cast-iron Body, Steel-hooped. 
— This mortar, Fig. 129, was designed before the 12-inch 
steel mortar, with the object of procuring a high-power 
B. L. mortar which would be cheap and could be made in 
large quantities. The value of mortar-fire depends on group- 
ing a large number of mortars in one place and under the 
control of one person, who can thus drop a number of pro- 
jectiles in a given area, and compensate by the number of 
shots for the lack of accuracy. Hence the necessity for 
cheapness. It is found, however, that the steel mortar has 
greater power and endurance, and it is possible that the 
manufacture of cast-iron mortars will be abandoned. 

The mortar consists of — 

The cast-iron body ; 
Five A hoops ; 
Six B hoops. 

The only point in the construction that requires notice 
is that the A h hoop is shrunk on the cast-iron body over two 
shoulders, ab. This is for the purpose of strengthening the 
cast iron longitudinally against the pull of the breech-block, 
and is similar to the method adopted in the 10 and 12-inch 

145. Breech Mechanism — Block — Obturator — Anti-friction Washers 
and Spring. 

The breech mechanisms of the 8, 10, and 12-inch guns 
are essentially the same. That for the mortar differs in 
some respects from the guns. 

The essential parts of the mechanism are : 

The breech-block ; 
The obturator ; 
The console or tray ; 

The device for rotating and withdrawing the breech- 
block ; 
The vent and vent-closer. 



Breech-block. — This resembles the blocks already de- 
scribed for the field and siege artillery. In the 8-inch gun 
there are three threaded and three slotted sectors ; in the 
10 and 1 2-inch, four. 

The rear end of the block is left unthreaded for some 


Fig. 130. 

distance, ab, Fig. 130. The cylinder of metal thus formed, 

fits accurately into the breech-recess, when the block is 

home, and prevents the entrance of sand or dust, which 

might cause jamming of the threads. 

Obturator. — This is the De Bange system modified, 

and differs from that used in the field and siege services as 

follows (Fig. 130) : 

The front cup is replaced by a split steel ring, c, shown in 

detail in Fig. 131, fitted against 
the outer portion of the mush- 
room-head. The rear gas-check 
cup is replaced by a flat disk of 
steel, d, fitting tightly against 
the front of the block. A split 
steel ring, e, similar to c, takes 
the place of part of the outer 
edge of the gas-check cup for- 
merly used, and another split 
FlG - I3I> ring,/, fits against the spindle. 

When the gas-pressure acts, these rings expand, and pre- 

GUNS. 26l 

vent the flame and gas from reaching the covering of the 
gas-check pad, and also from penetrating in the direction of 
the spindle. When the pressure is relieved the rings resume 
their normal size, and tend to cause the pad to leave its seat 
in the gun, and thus prevent sticking. 

Anti- friction Washers and Spring.— In all guns 
using the De Bange fermeture, the pad is liable to stick in 
its seat after firing, and render the breech difficult to open. 
This is provided for in the field and siege guns by the cam 
action of the head oi the lever-handle, as has been ex- 

In the sea-coast service, the lever-handle is not used for 
rotating the block, as it is not sufficiently powerful, and the 
following arrangement is adopted to overcome the sticking 
of the pad : 

By referring to the field-gun mechanism, it will be seen 
that there is a spring,/, between the obturator-nut h, Fig. 106, 
and the shoulder in the block. Hence when the block is 
rotated, it moves back \ of the pitch of its thread, compress- 
ing this spring and allowing the pad to remain fast in its seat. 
At the end of the rotation the cam action of the lever-handle 
draws out the pad from its seat. 

In the large guns, the spring is replaced by two anti- 
friction washers of steel, g, and two of brass, h, of the shape 
shown in Fig. 130. Each alternate washer is of brass, so that 
two metals of the same kind shall not rub against each other. 
A cup-shaped spring i tests against a shoulder on the front 
end of the obturator-nut j, and bears on the shoulder of the 
block. This spring acts as a cover to keep out dust. The 
action is as follows : 

When the block is rotated, it moves back \ or -J of the 
pitch of its thread. This brings a pressure upon the 
washers, which is thence transmitted to the obturator-nut, 
and by this pressure the pad is loosened in its seat. The 
object of the anti-friction washers is to allow this rotation 
of the block to occur independently of the spindle, and this 
is done by diminishing the lever-arm of the friction. 

3 /3 

r — r 
The value of this arm is, from mechanics, — ^-, in 

r 2 — r 



which r and r' are the exterior and interior radii of a ring. 
By giving a double-convex section to the washers, r is de- 
creased and r' increased ; and hence the moment of the fric- 
tion with reference to the axis of the spindle is sufficiently 
decreased to allow the spindle to stand fast while the block 

146. Apparatus for Rotating and Withdrawing the Breech-block 
— The Tray — The Translating Screw. 
Rotating Device. — The lever-handle cannot be used 
for rotating the breech-block in sea-coast guns owing to its 

Fig. 132. 

lack of power. The device adopted is called the " rotating- 
ring," and is shown in Fig. 132. 

It is a ring of steel encircling the breech-block, and hav- 
ing a lug, a, the exact width of one of the slotted sectors, 
projecting on the interior. This lug enters one of the 
slotted sectors of the block, and the remainder of the in- 
terior circle is of such diameter that the breech block will 
slide through it. On the exterior there is a projecting 
toothed sector, b, which gears into a pinion, p. When the 
pinion is rotated by a crank, k, motion is communicated 



to the rotating-ring, and through the lug a to the block. 
The rotating-ring is held in place against the rear face of 
the breech, by a steel plate, called the " breech-plate," 
which allows rotation, but prevents any other motion. The 
rotation of the ring and block is limited to an angle of 
6o° or 45 , according to the gun, by the surfaces c c' strik- 
ing against corresponding surfaces in the breech-plate. The 
rotation of the block having been completed, it can be 

Fig. 133. 

withdrawn from the breech, sliding through the rotating- 

The Tray or Console.— In the field and siege guns, 
the block, when withdrawn, is supported by a carrier-ring. 
In the sea-coast guns, this method will not answer, as the 
carrier-ring does not furnish sufficient bearing-surface to 
support the block. A tray is therefore used for this pur- 
pose, and is shown in Fig. 133. 

It is made of brass, and is hinged to the rear face of the 
breech, by a steel pin passing through the hub b. 



The tray swings around this pin, and with the block may 
be rotated to the right, out of the way for loading. 

Translating-SCREW. — Near the middle of the tray is a 

hole, c, which is threaded, and a 
slot c' is cut in its top, parallel to 
the axis of the hole. In this hole 
FlG - I34, c, works a double-threaded screw 

called the translating-screw, Fig. 134, the threads being 
right and left handed, and one of them 
narrower and more shallow than the 
other. The shallow thread engages 
in the corresponding thread in the 
hole c, Fig. 133, so that the screw 
when turned, will move in or out of 
the tray. On the rear end of the 
breech - block there is a projecting 
stud, b, Fig. 135, called the translating- 
stud. When the breech - block has 
rotated one sixth of a turn to the left, this stud moves 
down, and engages in the larger thread of the translating- 
screw. Hence when this screw is rotated, it withdraws the 
block from its recess with a motion equal to the sum of the 
pitches of the two threads, for each revolution of the screw. 

147. Remaining Farts of Breech Mechanism — Guide-rails — Guide- 
grooves — Side-latch — Tray Latch. 

On each side of the tray (Fig. 133) are two projections, 
aa' , equidistant from the screw. They are called the 

On the under side of the breech-block, at equal distances 
from the translating-stud, are two grooves, act! , Fig. 135, 
called " guide-grooves." These grooves do not extend the 
whole length of the block, but end abruptly at shoulders. 
When the block is withdrawn by the translating-screw, the 
guide-grooves slide on the guide- rails, which thus furnish the 
bearing for the block, and the block continues its movement 
to the rear till it is suddenly stopped by the striking of the 
shoulders of the grooves aa' on the front ends of the guide- 
rails of the tray. 

GUNS. 265 

During this motion of the block the translating-stud b, 
Fig- I 3S, travels in the slot c' , Fig. 133, being always engaged 
in the larger thread of the translating-screw. 

Side Latch.— When the block has reached the end of 
its travel, the tray and block are swung by hand to the right 
for loading. 

To hold the tray and block in this position, and prevent 
the accidental closing of the breech.'by the swinging in of 
the tray, a catch is provided on the under side of the tray, 
and a side latch on the breech of the gun. This latch catches 
the tray as it swings around, and retains tray and block till 
the latch is lifted by hand. 

Tray -LATCH. — When the tray and block are swung 
around after loading, into the position for the insertion of 
the block in the breech, the block is moved forward along 
the tray by the translating-screw. 

But in order that the block may enter its recess in the 
breech, the tray must fit accurately against the rear face of 
the breech, so that the guide-rails shall be parallel to the 
axis of the bore. 

Again, as soon as the block enters its recess and begins 
to bear on it, the thrust of the translating-screw will tend to 
move the tray back from the breech. There must be some 
arrangement, therefore, to latch the tray against the breech, 
and hold it in that position till the block is home, and this is 
the object of the tray-latch. This latch fits into a recess, d, 
Fig- l l?» hi the lower part of the tray, and engages in a cor- 
responding recess in the breech of the gun. It is shown in Fig. 
136. It is constantly acted on by the spring-lock c, which keeps 
it engaged in the recess in the 
breech of the gun. The upper 
end of this lock bears against 
the translating-screw in the 
tray, and hence the lock can 

rise and the tray be unlatched 

J Fig. 136. 

only when the end of the 

translating-screw is beyond the lock c. This happens when 

the block is withdrawn. The sudden shock of the block 

striking against the guide-rails in its outward motion, is 


communicated to the latch, and acting obliquely, a force 
perpendicular to the axis of the latch is developed, of 
sufficient intensity to disengage it automatically from the 

Fig. 137. 

148. Vent-cover— Action of Breech Mechanism. 

Vent-cover.— This consists of a flat piece of steel, a, 
Fig. 1 37, pivoted loosely in the breech-block. 

The head of this piece bears against the inner surface of 
the breech-recess as the block rotates, 
and hence it cannot move around the 
pivot, but remains in the same radial 
position covering the vent. At the 
end of the rotation of the block, when 
the threads are engaged in those of 
the breech-recess, the head drops into 
a groove cut for it in the breech 
recess, and the vent-closer assumes 
the position a', uncovering the vent. 
When the block is rotated to the left for unlocking, the first 
motion brings the head to its bearing against the breech-re- 
cess, and thus closes the vent. 

Action of Breech Mechanism — Breech Closed. — In this 
position of the block its threads are engaged in those of 
the breech-recess, the gas-check is in its seat in the tube, 
the vent-cover has moved to the right, uncovering the 
vent, the tray is latched to the breech by the tray-latch, 
and the translating-screw is in its recess as far as it will 

To Open the Breech. — Turn the crank attached to the pin- 
ion of the rotating-ring, in the direction indicated by the 
arrow on the breech. This motion is communicated to the 
rotating-ring through the toothed sector, and from this 
ring to the breech-block, by the lug which enters its slotted 
sector. As the block begins to rotate to the left, the vent- 
closer closes the vent as explained. When the block has 
rotated one sixth of a turn, the translating-stud enters the 
thread of the translating-screw in the tray. This screw is 
then rotated by its crank, and the block withdrawn from its 

GUNS. 267 

recess in the breech. At the end of its travel the shoulders 
on the block strike against the ends of the guide-rails on 
the tray, and the shock disengages the tray-latch from the 

Fig. 138. 

breech. The tray and block can now be swung around for 

To Close the Breech. — Lift the side latch; swing the tray 
and block around to the left till the tray-latch is engaged 


in its recess in the breech. The block is now driven home 
by the translating-screw. 

Rotate the block to the right by the rotating-crank, and 
when the rotation is finished, the block will be in the posi- 
tion first described and the gun ready for firing. 

The mechanism for the 10 and 12 inch guns is so similar 
to this that no special description is necessary. 

149. Breech Mechanism of 12-inch Mortar. 

In this piece the mechanism differs from that of the guns 
as follows : 

Rotating Device. — On the rear face of the breech-block is 
fixed a steel plate, k, Fig. 139, called a face-plate. The upper 

Fig. 139. 

end or stem of this face-plate is cut out, and carries two gears, 
a, b, and on the exterior a third gear, c, on the same shaft 
with b. Motion is communicated to these gears by the 
crank d. On the rear face of the breech is a circular rack e, 
with which the gear c engages, when the block is pushed 
home. It is evident that a rotation of the crank d will cause 
the face-plate and block to rotate to the right, or a reverse 
motion of the crank, when the breech is closed, will cause a 
rotation of the block to the left. The block is withdrawn 

GUNS. 269 

by a translating-screw as before. The tray-latch is the same 
in principle as in the guns, the only change in construction 
being that the spring-lock acts in front of the pivot, and the 
latch rises when it is disengaged. 

Vent-closer. — This resembles that used in the 3.2-inch 
gun, and consists of a piece of metal, /, sliding in a slot in 
the face-plate. A pin projecting from the front of this slid- 
ing-piece, bears in a groove g in the rear face of the breech, 
which is concentric for some distance with the axis of the 
breech-block, and at its lower extremity becomes eccentric. 
Its action in uncovering the vent is the same as in the case 
of the 3.2-inch guns. 

Action of Mechanism. — When the block is closed, the head 
of the face-plate is at the right-hand end of the rack e, the 
crank d is parallel to the axis of the face-plate, and is held 
in place by a spring-lock h. After firing, the crank d is 
turned, and the gear c engaging in the rack e, rotates the 
block to the left. 

The rotation of the block is limited, by the striking of the 
sides of the face-plate against the ends of the circular recess 
in which the rack is placed. The block is now withdrawn 
by the translating-screw, and block and tray swung round 
for loading. 

To close the breech the operations are reversed. 

150. Improved Mechanism — Continuous Rotation. 

Objections to Ordinary Mechanism. — In the mechanism 
already described, one crank is necessary to rotate the 
block, and at the end of this movement, the power must be 
transferred to another crank for withdrawing the block. 
When the block is withdrawn, the power must be applied 
to the handle of the tray to swing the block and tray 
around. We have thus three separate and distinct mo- 
tions, involving loss of time, and complication of mechan- 

Improvements. — In the latest improved mechanism, the 
object is to effect by the application of power to one crank, 
and by its continuous movement, the rotation, translation, 
and swing, of the block and tray. 



This mechanism, as applied in our service, is called the 
Farcot, from its inventor, and consists (Fig. 140) of the fol- 
lowing parts : 

On the right side of the rear end of the breech-block is 
a circular-toothed sector a. A cut is made in one of the 
threaded sectors of the block parallel to its axis, and this 
circular rack is extended along the block as shown in the 
figure (plan), the width of this longitudinal rack b being 
that of the thickness of the wheel c, while the width of 

Fig. 140. 

the circular sector a is one sixth of the circumference of 
the block. On the top of the hinge-pin d, is mounted a 
worm-gear c, whose teeth fit the corresponding teeth of the 
sector a. 

At the bottom of the hinge-pin d is a second worm- 
gear, e. A horizontal crank-shaft, f, has at the right end a 
worm, g, gearing into the worm-gear e, and at the left end a 
crank, h. 

Action of Mechanism. — When the crank h is turned, 
motion is communicated to the worm-gear c through g and 
e, and the action of c on the sector a rotates the block one 



sixth of a turn, till the shoulders kl on the block strike 
against the guide-rails mn. 

The block then being no longer able to turn, the teeth of 
the wheel c, engaging in those of the rack b, along the block, 
will force the block to the rear out of the breech-recess. 
The cut in the threaded sector of the block, for the reception 
of the rack b, is made so deep that the worm-wheel c binds 
against the edges of this cut in travelling along the rack, 

Table II. — Breech-loading Ordnance, U. S. Land Service. 

Calibre, inches 




Total length, feet 

Length of bore, calibres.. . 

Diameter over powder- 
chamber, inches 

Diameter of powder-cham- 
ber, inches 

Thickness over powder- 
chamber, calibres 

Number of cylinders com- 
prised in the thickness. , 

Maximum tangential resist- 
ance, pounds per sq. in.. 


Number of grooves 

Width of grooves, inches 
Depth of grooves, inches 
Width of lands, inches, 

Twist, calibres., 

Total capacity of bore, 
cubic inches 

Capacity of powder-cham- 
ber, cubic inches 

Lengthof powder-chamber, 

Travel of projectile in bore, 

Powder charge: 


Weight, pounds 

Density of loading 


Weight, pounds.. 

Ratio to weight of piece. 

Pressure in powder-cham- 
ber, lbs. per square inch 

Muzzle velocity, ft. -sees. .. 

Muzzle energy, foot-tons.. 

Penetration in steel: 

Muzzle, inches 

3500 yards, inches 

Seacoast Guns, Steel. 

1888, M. 

i 32.372 1 
! 32,480 f 











I x in 50 10 

( 1 in 25 








1 to 108 





:888, M. 





1 11. 8 

1. 13 







1 in 50 to 

1 in 25 








1 to 117 


14. 6 

1888, M. 









1 in 50 to 

1 in 25 





1 to 116 







37 83 









1 in 50 to 

1 in 25 







1 to 129 










1. 148 







in 50 to 

1 in 25 



106 . 06 


1 to 118 


64 ,084 

27 5 

Seacoast Mortars. 

Cast iron 















1. 18 











. 0.175 
1 in 40 to 

1 in 40 to 

1 in 25 

1 in 20 












J 800 

( 1,000 

1 to 40 


1 . T026 


1 to 36 








a U.R. brown prismatic, b W.H. brown prismatic, c V. P. brown prismatic, thrown 
prismatic; e V.M. brown prismatic. 


and hence any tendency of the block to rotate is overcome. 
When the block reaches the end of its travel, it strikes 
against the ends of the guide-rails and releases the tray- 
latch from its recess in the breech by the shock, as before 
explained. As the block is not able to move further on the 
tray, but is free to swing with the tray around the pin d, 
the pressure of the teeth of c against those of the rack will 
cause this swinging to take place, thus opening the breech 
for loading. 

A reversal of these motions closes the breech for fir- 

The table on page 271 gives the details with reference to 
the seacoast guns and mortars in the U. S. service. 

151. Old Guns in U. S. Service — 3-inch Wrought-iron Eifle — 
4.5-inch Siege-gun — 4.2-inch Parrott Siege-gun — 8-inch Con- 
verted Rifle — 15-inch Rodman Smooth-bore. 

3-inch Wrought-iron Rifle (Fig. 141). — This gun was 
used during the war of 1861-65, and is still found in service. 
n It is made by wrapping holler- 
ed C~~JZZ7r/~"l~ r//J71^^^^ iron around a wrought-iron 
9 mandrel, heating the resulting 
FlG - T 4 T - cylinder to a welding-heat, and 
passing it through the rolls. The gun is then bored, turned, 
and rifled. The object of the construction is to have the 
fibres of the wrought iron in the direction of the tangential 

stress. The objection to the construction is the liability to 
false welds. 

4.5-iNCH Siege-gun (Fig. 142). — This gun is made of cast 
iron, cast solid, and bored, turned, and rifled. It has given 
very good results, but is uncertain in strength, like all guns 



cast on this plan, and several accidents have occurred which 
have caused it to be abandoned. 

4.2-iNCH Parrott Siege-gun (Fig. 143). — This gun is 
also made of cast iron, but is reinforced at the breech by a 

Fig. 143. 

heavy jacket of wrought iron. This jacket was made by 
coiling a hot bar of wrought iron around a mandrel into a 
spiral, and welding the coils into a cylinder by blows from a 
hammer parallel to the axis of the cylinder. The cylinder 
was next bored, and then shrunk upon the exterior of the 
breech of the gun. At the time these guns were made, 
nothing was known about the theory of shrinkage as at pres- 
ent applied to guns, and hence the shrinkage was not prop- 
erly regulated, and was very often a source of weakness, 
especially at the junction of the front end of the cylinder 
with the gun. In spite of this, however, these guns have 
proved very serviceable. 

8-inch Converted Rifle (Fig. 144). — These guns were 
made for the purpose of utilizing a large number of old 10- 

Fig. 144- 

inch Rodman cast-iron, guns which were on hand, the idea 
being to render them more accurate and powerful, by con- 
verting them into rifled guns. This was done by boring 
out the 10-inch gun to a larger diameter, and inserting 


a tube into this bore. This tube was held in place by a col- 
lar, a, screwed into the cast-iron body and resting against a 
shoulder, b, on the muzzle end of the tube. The tubes were 
made at first by coiling bars of wrought iron around a man- 
drel, and welding them by axial blows. This method was 
abandoned on account of the false welds in the tube, which 
sometimes cracked and separated from this cause. The 
tubes were finally made of steel, and numbers of these guns 
are still in service. The rotation of the tube, due to the ac- 
tion of the projectile, is prevented by a pin, c, which passes 
through the cast iron body and enters the tube. 

15-iNCH Rodman Smooth-bore. — This gun is still re- 
tained in service, and is intended to be used with large 
charges of mammoth powder, as a secondary gun, for com- 
paratively short ranges, and against light armor. It is 
cast hollow on the Rodman plan ; its projectile weighs 450 
pounds, and the gun about 22 tons. 

152. Foreign Guns — Krupp Mechanism — Locking-screw. 

All heavy guns are built upon the same principles as 
those already explained, and hence a description 1 of th© guns 
of different countries is unnecessary. The only departure 
from the system above described, is in the case of the breech 

Krupp Mechanism. — While the French or interrupted- 
screw system has been adopted by most of the foreign na- 
tions, Germany, and some others, use the Krupp system. 

It has stood the test oi service and has been well and 
favorably known for many years, and hence will be described 

The jacket a, Fig. 145, extends to the rear of the tube, 
and carries the fermeture. A slot is cut transversely in the 
jacket just in rear of the tube. This slot, in front, is perpen- 
dicular to the axis of the bore, and is a plane surface, with 
corners rounded to avoid sharp angles. In rear, the sur- 
face of the slot is cylindrical, and the axis of the cylinder is 
inclined to that of the bore. Two guides, b b', are parallel 
to the axis of the cylinder. In this slot slides a breech- 
block, k, whose shape corresponds to that of the slot. It 

GUNS. 275 

Jias two recesses for the guides bb', and in the upper face, 
-a third recess, in which rests a long screw c, called the 
translating-screw. This screw is held in two collars in the 
breech-block, and works in a half-nut, d, on the gun. When 
the screw c is turned by a wrench, such as e, the block is 
drawn out of its recess or pushed home. 

Locking-screw.— In order to obtain a rapid motion in 
opening and closing the breech, the screw c is cut with a 
quick pitch. Consequently, 
there is very little power to 
press the gas-check firmly 
home, or, in opening the 
breech, to overcome any stick- 
ing that may occur. It is 
also necessary to have some 
method of locking the breech- 
block to the jacket in firing, 
to prevent accident. 

All these objects are ac- 
complished by the locking 
mechanism. This consists of 
a nut, f, and a screw, g. The 
nut has a series of rings, r, 
formed on its exterior sur- 
face. The outer ring is com- 
plete, the others are partially 
cut away. When the nut is 
turned so that, the^ cut-away 
portions of the rings are in 
rear, the surface of the nut 
coincides with that of the rear 
of the block. When turned 
120°, the parts of the rings 
not cut away project beyond 
the block and enter corresponding cuts in the breech. 
The nut has a small amount of travel along its screw g. 

Action. — The translating-screw c leaves the block not 
quite forced home. The nut /is at the bottom of its recess 
in the block, nearest the axis of the gun, and the cut rings 

Fig. 145. 

2 7. 6 


of the nut are turned to the rear. The wrench e is now 
applied to the screw g and the screw turned. This will 
cause the nut f to move along the screw, it being unable to- 
turn because of the cut parts of the rings bearing on the 
back of the transverse slot in the breech. As soon, how- 
ever, as the rings come opposite the cuts in the breech, the 
nut will turn, its rings entering the corresponding cuts in 
the breech, and after turning 120°, the pin h bears against 
a shoulder on the block, and stops the rotation of the. nut. 
As the screw still turns, the effect will be to cause the rings 
to bear against the cuts in the breech, and thus force the 
block home. At the same time the rings bearing in the 
cuts lock the block. A reversal of these operations opens 
the breech. ; 

153. The Gas-cheek — General Features of the Mechanism — Ad- 
vantages and Disadvantages. 
Gas-check. — With the Krupp mechanism, it is evident" 
that neither the De Bange nor the Freyre gas-checks can be 

used, since both of them must be 
drawn back from their seats in the 
gun, being attached to the breech- 
block. The Krupp block slides 
across the breech, and hence it is nec- 
essary to use a gas-check which can 
be left in the gun. The Broad well 
ring is used. It consists (Fig. 146) 
of two parts : the obturating-ring, 
a, and the obturator-plate, b. The 
exterior surface, cd, of the ring is 
spherical, so that it can be readily 
seated in the gun, and returned to' 
its place if it should become ,un- 
Fig. 146. seated. The surface c'd is plane, 

with a series of grooves to act as an air-packing, as before 
explained, and also to collect any dirt that may be on the 
surface of the obturator-plate. The obturator-plate b is of 
hardened steel, and is fitted into the face of the breech- 
block. The hollow e collects fouling, which, if the whole 










GUNS. 277 

front surface were plane, would be drawn against the edge 
of the obturating-ring when the block is withdrawn, and 
thereby increase the liability to fouling of the surface c'd. 
The surfaces c'c and c'd are those which must be kept sealed 
against the escape of gas. The surface c'd is especially 
difficult to seal, and hence the necessity for the heavy press- 
ure given by the locking-screw, to set the obturator-plate 
firmly against the ring. 

Action. — The gas acts upon this ring to force the thin 
edge c against the walls of the bore, and also to press the 
ring backwards against the obturator-plate, forcing down 
especially the edge d. 

General Features of Mechanism. — The locking- 
screw just described is supported at its outer extremity 
by a plate, k, Fig. 145, called the locking-plate. The 
travel of the block is limited by a chain, or by a stop-bolt 
which passes through the upper part of the breech, and 
projects into a groove in the block. The jacket is bored 
out in prolongation of the bore, for the insertion of the 
projectile and charge in loading, and this hole is also 
made through the breech-block, so that when the block 
is withdrawn the hole through it is also in prolongation 
of the bore. The rounded shape of the rear of the block, 
and of the slot, gives strength by avoiding sharp corners, 
and the inclination of the axis of the cylinder to that of 
the. bore, with that of the guides, gives a component mo- 
tion of the block parallel to the axis and gradually seats 
the block firmly, while" by a slight motion outward, all 
the parts become free and the block is easily with- 

Advantages. — The Krupp mechanism is very simple 
and not liable to get out of order. It has been thoroughly 
tested, and found to be reliable. If it becomes stuck or 
wedged in the gun, it may be more easily removed than the 
screw, as it is more accessible. 

Disadvantages. — It requires a heavier forging for its 
jacket than the screw system, and consequently increases 
the weight of the gun for the same length of bore. The 


Broad well ring is not as good a gas-check as the De Bange- 
or Freyre. 

The longitudinal stress is not uniformly distributed over- 
the cross-section of the jacket, and this is seen by a ten- 
dency of the gasrcheck seat to become oval, the longer axis. 
being parallel to that of the slot. 

It is more exposed to a front fire when open. 

It tends to guillotine the cartridge. 




154. Classification— Solid Shot— Chilled Shot— Steel Shot. 

Classification. — Projectiles may be classified according 
to their structure, as solid shot, shell, and case-shot ; accord- 
ing to their use, into field, siege, and sea-coast projectiles ; 
and according to their shape, as spherical and oblong. 

Spherical projectiles are now obsolete. 

Solid Shot. — Solid shot were formerly used for armor- 
piercing, and are still used in small arms against animate 
Objects. The advantages of solid shot are, that they have 
greater weight for the same volume, and hence greater 
energy for a given velocity ; and where it is necessary to 
concentrate energy upon a given area, as in attacking an 
armor-plate, they were generally employed. 

The disadvantages are that for attacking armor, the pro- 
jectile must possess great hardness to penetrate, and great 
toughness to resist breaking up on impact, and if the shot 
be made solid, it is subjected to initial strains due to casting 
or forging, which cannot be removed ; the metal in the in- 
terior is not sound, and hence we obtain weaker projectiles 
when solid than when they have an interior cavity or core. 
This cavity removes the unsound metal, if the projectile is 
of cast iron, or if of steel, allows it to be treated, so that the 
strains can be removed and toughness attained. Such shot 
are generally called " cored shot." 

The only solid projectiles at present in general use are for 

small arms. 





Chilled Shot. — With the introduction and improve- 
ment of wrought-iron armor, cast-iron projectiles became 

useless, as they were broken 
on impact. This led to the 
introduction of chilled cast- 
iron projectiles. The Palliser 
projectile, so called from its 
inventor, Major Palliser of 
the British Army, was for a 
long time quite celebrated, 
and very effective against 
*~> wrought-iron armor. 

It was made by casting 

Fig. 147. 
the ordinary cored shot in a chill, Fig. 147. 

The body of the projectile is cast in sand to give tough- 
ness, and the head in a cast-iron mould or chill a, so called 
because it carries off the heat of the parts in contact with it 
so rapidly as to cause chilling, and produce great hardness. 

The exterior of this chill conforms generally to the shape 
of the head, to insure uniform cooling, and it is lined with a 
movable lining, b. 

The latter soon becomes worn from contact with the 
heated metal, and is removed and replaced by a new lining, 
thus preserving the body of the chill a. The head of the 
chilled shot is shown at c. 

Steel Shot. — As armor improved in its resisting quali- 
ties, the chilled cast-iron projectile was broken on impact, and 
steel shot were substituted. The best of these are made of 




Fig. 148. 

chrome steel, forged and tempered. Two processes, known 
as the Holtzer and Firminy, are so far the best, but they are 
secret, and nothing is known of them. The projectiles made 


"by these processes give the best results when used against 
modern steel armor, but they are very expensive, and hence 
attempts are now being made, with some appearance of 
success, to replace them by cast-steel projectiles, which are 
tempered by a secret process. 

Fig. 148 shows a forged-steel Holtzer armor-piercing 
cored shot. 

155. Shell— Definition— Shell for Sea-coast Service— Deck-piercing 

Definition. — A shell is a hollow projectile, containing a 
bursting charge of gunpowder, or some high explosive, and 
a fuze to ignite this charge at some point of its flight, or 
upon impact. 

Shells are used in the sea-coast, siege, and field services, 
and their construction depends on the purpose for which 
they are intended. 

Shells for Sea-coast Service.— In the sea-coast ser- 
vice, shells are used in high-powered guns for attacking 
armor, or in mortars with high angle-fire for piercing the 
decks of vessels. 

Against Armor. — If the shells can be made strong enough 
to penetrate armor, they are preferred to shot, because they 
burst after penetration, and acting in a confined space on a 
ship, cause great destruction. For this purpose the walls of 
the shell must be strong, and hence the cavity small. The 
cavity being small, will not contain a large bursting charge 
of powder, and the walls of the shell being strong, the gases 
from this charge may not develop sufficient pressure to rup- 
ture them. 

On this account, and because of its greater destructive 
effect, a high explosive as a bursting charge is necessary. 

Gun-cotton has been tried as a bursting charge for these 
shells. While it has given good results in some cases, it is 
liable to premature explosion from shock and friction, and 
if desensitized by moisture or by paraffine, it requires a 
strong primer of dry gun-cotton to detonate it, and this 
primer is liable to detonation by shock. The same principle 
applies to nearly all the high explosives which have been 



tried, and hence the problem of a suitable high explosive 
for armor-piercing shell is not yet solved. This has led to 
the introduction of various methods of firing high explosives, 
as the pneumatic dynamite gun, etc. 

With armor-piercing shell, it is sought by various means 
to delay the action of the bursting charge till penetration is 
complete, as by wrapping the charge in flannel, using de- 
layed-action fuzes, etc. 

Against the Decks of Vessels. — The problem of pen- 
etrating the sides of armored vessels being so difficult, at- 
tempts are made to perforate their decks. When the weight 
of guns, machinery, and armor carried by ships of the pres- 


Fig. 149. 

ent day is considered, the available weight left for deck pro- 
tection is comparatively small, and hence a thickness of about 
4J inches of protective deck is about all that can be carried. 
Against these decks, the vertical fire of shell from heavy 



Fig. 150. 

rifled mortars is directed. The shells for these mortars do 
not require great strength of wall, since the thickness to be 
penetrated is so small, and hence they may be made of cast 
iron, with great interior capacity. They carry heavy burst- 
ing charges, and their effect is very destructive. The dis- 
advantage is, the difficulty of hitting the object. As the 
shells are fired with comparatively low charges, the dangers 


of premature explosion from shock are lessened, and recent 
experiments at Sandy Hook have shown that high explo- 
sives can be fired from these mortars with safety. At pres- 
ent these shells are made of forged steel. 

Figs. 149 and 150 show a steel deck-piercing shell and a 
cast-iron shell for the 12-inch mortar. 

156. Siege Shell— Field Shell. 

Siege shell. — The shells for siege purposes are some- 
what similar to those for deck piercing. They are used in 
direct and curved fire, and against earth or masonry. Their 
object, therefore, is to displace the earth and masonry, and 
as no great strength is required against these obstacles, the 
siege-shell are made of cast iron. In firing against masonry, 
it is necessary not only to penetrate, but also to remove the 
broken fragments, so that the next shot may fall upon a 
fresh surface. For this purpose large bursting charges are 
required, and hence large cavities, and comparatively thin 
walls. Very long shell are sometimes supplied for this pur- 
pose, and are called " torpedo shell." 

Against earth, the maximum displacement is required, 
and some experiments made with gun-cotton as a bursting 


Fig. 151. 

charge show that it is very effective. The 5-inch siege shell 
is shown in Fig. 151. 

Field Shell. — In field artillery the objects to be at- 
tacked have little resistance, as they are generally light field 
entrenchments, buildings, or troops, and hence the effect 
depends on the number of fragments into which the shell 

The number of these fragments will depend on the 
brittleness of the material, and the pressure of the gases 


from the bursting charge, at the time when rupture 

The natural tendency of a shell is to burst in a meridian 
plane, or a plane through its longer axis, since the total 
pressure of the gases normal to this plane is greater than 
that normal to the transverse plane. If the pressure of the 
gases is developed slowly, as from a bursting charge of 
large-grained powder, rupture will occur as just indicated, 
and we will have a few large fragments, and the effect will 
be limited. To avoid this it is necessary — 

1. -To use as a bursting charge, fine-grained powder of 
high gravimetric density. By this means the pressure is 
rapidly developed, and the largest possible weight of charge 
is contained in a given volume. 

2. To prevent rupture in a longitudinal plane, the interior 
of the shell is sometimes grooved spirally, to weaken it, and 
give more fragments. A remaining velocity of 500 ft.-secs. 
is generally considered sufficient to disable or kill a man, 
and a fragment weighing about 1 ounce with this velocity 
is effective. With the 13.5-lb. shell this would give 216 
effective fragments, and with the 20 lb. shell 320. In prac- 
tice these results cannot be obtained. 

Owing to the irregularity of their action, field-shells are 
seldom used against animate objects, except at very long 
distances, or when under cover. They are used, however, 
with percussion fuzes, to obtain the range quickly. By 

firing a percussion shell with a 

certain elevation, so as to strike in 

, front of the target, and again with 

3 20 INCH riCLD SHELL / . -i , ■ 

cast iron _^^ an increased elevation, so as to 

Fig. 152. strike beyond it, and observing 

the points of burst, the target is 
thus enclosed in a fork, and by working between these lim- 
its, the true elevation is soon obtained. The 3.2-inch shell is 
is shown in Fig. 152. 

157. Case-shot — Grape — Canister. 

Definition. — Case-shot may be defined to be a collec- 
tion of particles enclosed in a case or envelope, the latter 



being intended to rupture in the gun, or at some point in 
flight, and liberate the enclosed particles. 

According to the place of rupture of the envelope, case- 
shot may be divided into — 

1. Grape ; 

2. Canister, 

whose envelope is broken in the gun, by the shock of dis- 
charge ; and, 

3. Shrapnel, 

whose envelope is broken at some point of the flight of the 

Grape. — This projectile is no longer used, but is interest- 
ing historically. It consists of three layers of balls, each 
layer containing generally three balls (see 
Fig. 153) held in place by top and bottom 
plates, a and b, of iron ; a central bolt and 
nut, c; and two intermediate rings, dd. It 
was used in the sea-coast service with 
smooth-bore guns, against the masts and 
rigging of ships, and against men ; also in 
the siege and field services against ani- 
mate objects in mass, at distances too 
great for smaller projectiles. 

Canister. — This con- 
sists (Fig. 154) of a number of spherical bullets 
of lead hardened with antimony, or of cast 
iron, contained in a can; hence the name. 
The envelope is closed by a top and bottom 
plate of iron, and is intended only for conven- 
ience in transportation, and in loading. 

It was used principally in the field service 
with the old smooth-bore guns, against ani- 
mate objects at close range. 

In both these projectiles, the case rup- 
tured in the bore, and the projectiles scattered at the muz- 
zle, forming a cone of dispersion, with its apex at the latter 

For rifled guns it was necessary to prevent the case 
taking the grooves-, and thus giving it the rifled motion 



Fig. 153. 


and increasing the lateral dispersion of the projectiles, 
which was already great. 

For this purpose the case was made stronger, 
since with the tin case, the projectiles were forced 
sidewise by the shock of discharge, expanding 
the case, and forcing it into the grooves. In our 
service this was done by adopting the Sawyer 
canister, the case of which is made of malleable 
cast iron, weakened by spiral cuts, as shown in 
Fig. 1 55, so as to insure its breaking up in the gun. 

All these projectiles were used at short range, 
and since the fighting range has been increased, 
owing to the longer range and higher ballistic 

Fig. 155. power of small arms, the) r are little used a>t the 
present day. A few rounds of canister are sometimes car- 
ried with the field gun for emergencies. 

158. Shrapnel — Cone of Dispersion — Causes which Affect it 

Shrapnel. — This projectile is now the most important in 
field artillery, and is employed to the exclusion of all others. 
It consists essentially of a case or envelope containing small 
round projectiles, and a bursting charge, and fuze. The 
charge is sufficient to rupture the envelope at a given point 
of flight of the projectile, the fuze being arranged to ignite 
the charge at that point. After the rupture of the envelope, 
the contained projectiles move on with a velocity which is 
the resultant of that due to discharge, and to the bursting 
charge, and act from the point of burst to the target, as 
canister. The object of the envelope then is to convey the 
small projectiles to within striking distance of the target, 
where they are liberated, and each particle acts. The pro- 
jectile is used entirely against animate objects, and its advan- 
tages over the shell are that the division of the particles is 
made beforehand, and each one is of the proper size to exert 
a disabling or killing effect. 

Cone of Dispersion.— When rupture of the case occurs, 
each contained particle describes its own path, and the 
paths thus described, taken together, form the elements of 
the " cone of dispersion." The intersection of this cone with 


the ground is an irregular oval, and its area will vary 
with — 

Causes which Affect it. — i. The angle of elevation of 
the piece ; 

2. The velocity of translation of the shrapnel before 
bursting ; 

3. The velocity of rotation of the shrapnel before bursting; 

4. The position of the bursting charge ; 

5. The height above the ground at which the shrapnel 

Angle of Elevation. — If this be large, other things being 
equal, the angle of fall will be large, and the plane of inter- 
section being more nearly normal to the mean axis of the 
cone of dispersion, the area of the oval will decrease ; the 
converse is true for small angles of elevation (see Fig. 156). 

Fig. 156. 

Velocity of Translation. — The greater this velocity, the 
greater will be the velocity of the particles in the plane of 
fire, and consequently the longer the oval in this direction. 

Velocity of Rotation. — This causes the particles to move 
at right angles to the plane of fire, and hence increases the 
lateral dispersion of the particles, and the width of the oval. 

Position of Bursting Charge. — This may be in front, or in 
rear of the particles. If in front, it decreases the velocity 
of translation of the particles, and hence decreases the length 
of the oval, and for this reason its effect is injurious. For 
other reasons, however, the position is a good one, as will 
be seen. 

When in rear, it increases the velocity of the particles in 
the plane of fire ; but there are objections to this position. 

Height of Burst. — It is evident that, for a given inclina- 
tion, and for given velocities in the plane of fire and later- 



ally, the higher the point of burst, the greater the area of 
the oval. 

The constant tendency with shrapnel is to increase the 
velocity of the particles in the plane of fire, and to decrease 
that at right angles to this plane ; and the best possible con- 
dition for the efficiency of this projectile is when the area 
of the oval is such that each bullet will hit a man.. The 
best position for the point of burst is about 6 yards above 
and 50 yards in front of the target. 

159. Construction of Spherical Shrapnel — Early Shrapnel — V. S.. 
Spherical Case — Boxer Spherical Shrapnel. 

Spherical shrapnel is now obsolete, but the history of 
its development shows clearly the directions in which im- 
provements have been made. 

Early Shrapnel. — The projectile was invented by 
Colonel Shrapnel of the British Army, about 1803. In its 
early form it was simply a spherical shell filled with bullets, 
and the bursting charge was contained in the interstices be- 
tween them. The objections to this arrangement were : 

1. When the projectile was fired the balls spread side^ 
wise, and tended to deform or burst the shell. Hence the 
latter was made with thick walls to resist this force, and 
this decreased the interior capacity, and consequently, the. 
number of bullets which it would contain. 

2. The powder, being loose among the bullets, was sub-, 
jected to trituration and friction in handling, and hence 
was liable to accident. Since the space between the bullets 

was large, the density of loading of 
the bursting charge was low, and 
hence a large bursting charge was 
required to rupture the envelope. 
This scattered the fragments too 
much, and rendered the action of the 
fuze more irregular. 

U. S. Spherical Case. — These 
defects suggested the improvements 
which were made in the spherical, 
shrapnel used during the Civil War (Fig. 157): 


i. To prevent the spreading of the bullets, the shell was 
first filled with them, and melted sulphur was then poured 
in, filling the interstices between the bullets. They were 
thus converted into a solid mass, and as their tendency to 
spread sidewise was thus destroyed, the case was made 
thinner, and consequently held more bullets. 

2. To diminish the bursting charge, a cylindrical hole 
was bored through the bullets and sulphur, and in this the 
bursting charge was placed. Thus the density of loading 
was increased, and a small bursting charge could be used 
with less uncertainty in the action of the fuze. 

The objections to this arrangement were that the sul- 
phur caused the bullets to stick together, and prevented 
their separation after the bursting of the case, and that the 
effect of the bursting charge was to increase the lateral 
dispersion of the particles. 

Boxer Spherical Shrapnel. — Most of the defects in 
the above shrapnel were remedied in the Boxer Spherical 
Shrapnel (Fig. 158), invented by 
Colonel Boxer of the English Army. 

In this projectile, the bursting 
charge was placed in a chamber, a, 
formed by introducing a wrought- 
iron diaphragm, b, into the mold be- 
fore casting, and allowing the cast 
iron to cool around it. The bullets 
were introduced through the open- 
ing c, the upper end of which carried 
the fuze, the flame from which reached the charge through 
a hole, d. The sulphur used as packing in the U. S. shrap- 
nel, was replaced by coal dust. 

This shrapnel possessed the following advantages : 

1. The bullets did not adhere to the matrix after burst- 

2. A small bursting charge could be used. 

3. The diaphragm b weakened the case, so that it would 
burst readily. 

4. As soon as the shrapnel left the piece (since its for- 
ward portion, which contained the fuze, was lighter than 

Fig. 158. 



the rear portion), the lighter portion would turn to the rear, 
leaving the centre of gravity in advance of the centre of 
figure. This brought the bursting charge in rear, and 
hence, on explosion, it acted to increase the forward ve- 
locity of the bullets, and its tendency to scatter was very 

160. Oblong Shrapnel — Boxer — Modern Shrapnel — Position of 
Bursting Charge. 
Boxer Oblong Shrapnel. — At this point the develop- 
ment of spherical shrapnel ceased, owing to the introduction 
of rifled guns and oblong projectiles. 
The first oblong shrapnel of any import- 
ance was that of Colonel Boxer. This 
consists (Fig. 159) of a cast-iron body, a ; 
and a wooden head, b, covered with 
sheet-iron, c, riveted to the cast-iron 
body. The bursting charge is contained 
in the chamber d in rear, and over this 
chamber, separating the charge from 
the bullets, is a cast-iron disk, e. The 
central tube /is filled with powder, and 
conveys the flame from the fuze g, to the 
bursting charge d. The balls are held 
together by melted resin, and a paper 
lining prevents the adhesion of the 
matrix to the walls of the envelope. 

This shrapnel has the following ad- 
vantages : 

1. Those common to all oblong pro- 
jectiles — of greater range and accuracy, 
and, for a given cross-section, containing a larger number 
of projectiles than the corresponding spherical shrapnel. 

2. The charge, being in rear, acts, as with the Boxei 
spherical shrapnel, to increase the forward velocity of the 
bullets after rupture. 

3. The head and its attachments, being relatively weak, 
give way easily, and the bullets are swept out to the front 
by the rear disk e ; the action in this respect being like the 
discharge of canister. 

Fig. 159. 


The disadvantages are : 

1. The body being of cast iron, the walls are made com- 
paratively thick to withstand the shock of discharge, and 
this reduces the interior capacity, and consequently the 
number of bullets which the shrapnel contains. 

2. The wooden head takes up room which can be better 

3. The delay caused by the communication of fire from 
the fuze to the bursting charge may interfere with the 
action of the shrapnel, and cause it to pass beyond its 
proper point of burst before exploding. 

4. The effect of the pressure of the gases from the 
central tube, is to cause an increase in the lateral spread of 
the bullets, which is objectionable. 

Modern Shrapnel. — These disadvantages suggest the 
improvements which have been made in modern shrapnel. 
Several of these are now under trial in this country. The 
following changes have been made in them, in comparison 
with the Boxer oblong shrapnel : 

1. To give sufficient strength of wall to withstand the 
shock of discharge, the body is made of drawn-steel tubing, 
and the head and base are welded on by electricity. As this 
is an expensive construction, wrought-iron tubing has been 
substituted for the steel, and the head and base are made of 
cast iron screwed into the wrought-iron body. 

2. In case the bursting charge is in front, as in one of the 
shrapnel undergoing trial, a cast-iron chamber takes the 
place of the wooden head of the Boxer, and contains the 
bursting charge and fuze. 

3. To lessen the delay caused by communication of fire 
through the central tube to the rear bursting charge, this 
tube is enlarged on the interior, and made of brass tubing 
so as to give a larger channel for the passage of the flame, 
and it does not occupy more space in the shrapnel, as the 
exterior diameter of the tube is not changed. 

4. To prevent adherence of the balls after rupture, the 
matrix is made of cast iron, indented so as to hold the balls 
in place and form a solid mass with the projectile, and yet 


so arranged as to break up into fragments when the shrap- 
nel bursts, which add their effect to that of the balls. 

Position of Bursting Charge.— When the bursting 
charge is in front, we have the following advantages : 

1. It occupies less space in the shrapnel, since no central 
tube is required ; 

2. It acts promptly to burst the case, and hence the point 
of burst can be more accurately fixed ; 

3. It occupies space in the shrapnel which it is difficult 
to fill with bullets. 

Its disadvantage is : 

1. It decreases the velocity of the fragments in the plane 
of fire, instead of increasing it. 

When the bursting charge is in rear, it has the advan- 

1. It increases the velocity of the fragments in the plane 
of fire. 

Its disadvantages are : 

1. It occupies increased space in the shrapnel ; 

2. It causes delay in bursting ; 

3. It increases the lateral spread of the fragments ; 

4. It is more expensive in construction. 

For these reasons it is probable that the front charge 
will be adopted, but it is not yet settled. 

161. Description of Modern Shrapnel — Steel-welded — Frankford 

Steel-welded. — The steel-welded shrapnel (Fig. 160) 
consists of a steel tube, a, to which the base b and head c 
are welded by electricity. The charge is in rear, and is 
separated from the bullets by a disk, d. The central tube 
communicates fire to the charge from the fuze. The bul- 
lets are held in place by a matrix of resin, melted and poured 
in after the former are in place. 

The Frankford Arsenal. — This shrapnel (Fig. 161) 
consists of a wrought-iron tube, a, to which the base b of 
cast iron is screwed. The rotating band c fits in a groove 
cut on the rear end of the tube a. The head d is also of 
cast iron, carries the bursting charge and fuze, and is 



screwed to the body. The bullets are held in place by a 
skeleton matrix of cast iron, consisting of a top and bottom 
plate, and a series of intermediate plates. 

These intermediate plates are made in segments, so that 

the whole can be built up layer 
by layer, and inserted in the 
body of the case. The head 
and base are then screwed on, 
the band being inserted in its 
groove before the latter is 
screwed home. This shrapnel 

Fig. 160. 

Fig. 161. 

is much cheaper than the steel one, and has given good 
results at the Proving Ground. 

The Hotchkiss shrapnel is similar to this. 

162. Necessity for Rotation of an Oblong Projectile — Energy of 
Rotation Required. 

Necessity. — It has been shown that an oblong projec- 
tile when rotating about its longer axis, will move through 
the air in the general direction of that axis. 

Without this motion of rotation about the longer axis, the 
resultant resistance of the air, acting with a certain lever 


arm, will cause the projectile to rotate about a short axis 
through the centre of mass. 

The effect of this would be to cause great irregularity of 
motion, owing to the varying surface presented to the air 
by the projectile, during this rotation. 

The rotary motion about the longer axis is imparted 
to the projectile by cutting spiral grooves in the surface of 
the bore, and by placing a device upon the projectile which 
will fit in these grooves, and thus cause the projectile to 
take up the rifled motion. 

Energy of Rotation. — The question as to the amount of 
energy of rotation about the longer axis which the projectile 
must have, to enable it to maintain its proper position dur- 
ing flight, requires for its determination analytical methods 
which are too complex to be given here. A general discus- 
sion will show upon what principles it depends. 

163. General Discussion of the Rotation of a Projectile— Value of R. 

The general discussion of the motion of rotation of an ob- 
long projectile, based upon Euler's equations, shows that for 
a projectile rotating from left to right, as in our service, the 
longer axis in the time t will deviate to the right of the 
plane of fire through an angle, cj>, whose value is 

Rl . , 

* = /£' ( 2 4 2 > 

in which (see Fig. 162) R is the resistance of the air acting 

at the centre of pressure, / 
its lever-arm with reference 
to a horizontal axis through 
the centre of gravity, / the 
moment of inertia about the 
longer axis of the projectile, 
and 00 the angular velocity about the same axis. 

In order that the projectile may be stable, Rl must be small 
and Iod large. The methods of decreasing R will be explained. 
In order that / may be small, the centre of mass and cen- 
tre of pressure must coincide as nearly as possible. The best 
position for the centre of mass is determined by experimen- 


tal firing, the projectile being so weighted that this centre 
can be changed. 

To increase /, the diameter of the projectile n ust be in- 
creased, its weight remaining constant ; or its mass or weight 
may be increased, if its dimensions are constant, by increas- 
ing the density of the material of which it is made. 

00 may be increased by giving a more rapid twist to the 
grooves in the gun, but this is limited by the increased 
strain brought upon the gun, and upon the projectile. 

Equation (242) shows, generally : 

1. As / increases, (p increases ; and since / depends on L, 
the total length of the projectile, if we increase the length 
of the projectile, we must increase /or 00, or both. 

Therefore generally a long projectile must have greater 
angular velocity about its, longer axis, than a short one of 
the same calibre. 

2. If two projectiles have the same length but different 
diameters, the value of / will be greater for the larger pro- 
jectile, and hence 00 may be less. That is, the projectile of 
greater diameter will require less angular velocity about its 
longer axis, than the projectile of smaller diameter and the 
same length. 

3. If we have two similar projectiles of different densi- 
ties, the dense projectile will require less angular velocity 
about its longer axis, since its mass, and hence its moment of 
inertia, is greater. Also, a shell will be more stable and re- 
quire less angular velocity than a similar shot of the same 
weight, since its radius of gyration is greater. 


4. Since = -j—t measures the deviation of the longer 


axis in the time /, the reciprocal, -=-., may be taken as the 

measure of the capacity of this axis to resist deviation ; and 

for a given value of R at any time t it is evident that by 

increasing the value of the ratio —r we increase the stability 

of the projectile. 

Value of R. — The resistance of the air, R, varies with 
the form, cross-section, and velocity of the projectile, and 


with the density of the air. The resistance being- R, the 
retardation produced by this resistance will be 


M being the mass of the projectile. 

This value of the retardation has been determined by 
experiment, as will be explained in Exterior Ballistics. 

In these experiments, the expression for -^ has been as- 
sumed to be (equations (263) and (265), Exterior Ballistics) 

R A , „ S aP , v 

M = C AV)=A J 1 W /{V) ' " • • • ( 2 43) 

in which A, .-, and c are constants, whose values are ex- 
plained in Exterior Ballistics, and / (v) is some function of 
the velocity of the projectile. Hence we may write 

R d" 

M =K W /{V) (244) 

For a given value of v, the retardation increases with the 

factor rr—\ and hence this factor must be made as small as 

possible, by increasing Wand decreasing d. The reciprocal 

of this factor, —^, may then be taken as a measure of the 

capacity of the projectile to overcome the resistance of the 

air, just as — — measures its stability. 

164. Sectional Density— How it May be Increased — Effect of its 
Increase on the Gun. 

Sectional Density. — The factor — is called the " sec- 
tional density" of the projectile. The area of base being 

\nd', — — will be the weight of the projectile per unit area 



of base, and hence — t is taken as a measure of this weight, 

the constant factor \n being omitted. The sectional density 
is very important in considering the motion of a projectile 
in air, and also in the gun. 

If two projectiles have the same initial velocity, but 
different sectional densities, that having the greater sec- 
tional density will be less retarded by the air, equation (244), 
and consequently will lose less velocity. Hence for a given 
range, its time of flight will be less, and being exposed to 
the action of the air, and other deviating causes, for a less 
time, its accuracy will be greater. 

If the two projectiles be fired with the same angle of 
elevation and the same initial velocity, that having the 
greater sectional density will have the greater range, since 
it retains more velocity at the end of each successive inter- 
val of time. 

For the same initial velocity, the trajectory or path of 
the projectile having the greater sectional density, will be 
flatter or less curved than that of the other, because since 
its velocity is greater at any point of its path, its time of 
passage over a given distance is less, and consequently the 
time during which the force of gravity acts upon it to pro- 
duce curvature is less. This gives greater accuracy of fire. 

An increase of sectional density therefore increases — 

1. The accuracy ; 

2. The range ; 

3. The flatness of the trajectory. 

How it May be Increased. — The sectional density 
may be increased by increasing W or by decreasing d. W 
may be increased by keeping the calibre constant, and in- 
creasing the length of the projectile. This has been done 
with modern projectiles, for large guns, till the length is 3J 
to 4 calibres. 

It may also be increased by increasing the density of the 
metal of which the projectile is made. This is done by 
using lead for small-arm projectiles, but this material does 
not possess sufficient hardness for projectiles for larger 


The sectional density may also be increased, by fixing- 
the weight W, and decreasing the calibre, or d. This 
method has been adopted for small arms, the calibre and 
weight of projectile having both been reduced in such pro- 
portions as to increase the sectional density. 

Effect of Increase of Sectional Density on the 
Gun. — Let P represent the maximum pressure per square 
inch on the base of the projectile ; 
M, the mass of the projectile. 

Then we have 



m -jt = nrjf, . 

from which 

dv itr>P Ttr'P 


dt ' M W 

~W ' 

' ' 



Replacing r by its value \d, 

dv Pg 

dt 1 w y " 
4W / 


As the sectional density -^-increases, -j- decreases, and 

hence to obtain an increase of acceleration, the value of P, 
or the pressure on the projectile, and consequently that 
upon the gun, must increase. Since the maximum pressure 
is fixed by the strength of the gun, equation (247) limits the 
value of the sectional density, for a given acceleration. The 
initial velocity is 

"dv 7 
dt dt -' < 2 4 8 > 

and for a given value of P, this velocity will decrease, from 
equation (247), as the sectional density increases. Hence 
when rifled guns were first introduced, using the old quick 
powders, the pressures could not be increased, and conse- 
quently the initial velocities of the projectiles decreased. 
When slow-burning powders were adopted, with longer 


bores, the sectional density of projectiles was increased, and 
also the initial velocities, with less maximum strain on the 
gun. The reason for this has been explained in Interior 

1 65. Rifling — Kinds — Uniform — Increasing. 

Rifling. — In order to give to the projectile the angular 
velocity oo required in equation (242), it is necessary to cut 
spiral grooves in the bore of the gun, and to attach a device 
to the projectile which will fit these grooves. The spiral 
groove in the gun is called the rifling. 

Let v denote the velocity of the projectile at any point 
of the bore ; 
<p, the angle made by the tangent to one of the 

grooves, with an element of the bore ; 
r, the radius of the bore. 

The velocity of the projectile along the groove, is the 
resultant of two components, v, and v tan <p, at right angles 
to each other. 

The actual velocity of rotation of a point on the surface 
of the projectile is oor, and this is equal to the component 
v tan 0. Hence 

a>r = v tan <p ; .-. 00 = — tan 0. . . . (249) 


Uniform Rifling or Twist. — If the value of <t> be 
constant for the whole length of the bore, the rifling or 
twist is said to be uniform. 

In this case the angular velocity varies directly with v 
and inversely with r. The objection to uniform rifling is as 
follows : 

When the projectile starts from its seat, and during the 
first part of its path in the bore, the pressure of the powder- 
gas rises to its maximum, and the gun is subjected to the 
greatest stress at this time. 

With the uniform rifling, the angular velocity 00 is im- 
pressed upon the projectile at this time also. Hence, while 
the gun is subjected to its greatest stress, due to the start- 


ing of the projectile, it is also subjected to its greatest stress 
in giving rotation to the projectile. 

After rotation is once acquired, the stress due to this 
cause falls off very rapidly. Therefore, with the uniform 
twist, both these stresses act together. 

Increasing Twist. — If, however, the angular velocity w 
be imparted gradually to the projectile, it moves from its 
seat more readily, and the strain on the gun at first is thus 
diminished. When the powder pressures fall off along the 
bore, the twist, or value of <fi, gradually increases, till it 
reaches its final value necessary to impart the angular 
velocity oo to the projectile. In this case the stresses are 
more uniformly distributed along the bore, and the gun 
strained less at the origin of motion, while the final velocity 
of rotation is the same. 

The twist in this case is called an increasing twist, as the 
value of <(> increases gradually from the breech. In modern 
guns the curve of the rifling, when developed on a plane 
surface, is a semi-cubic parabola, whose equation is 

ji = 2px. 

To give steadiness of rotation to the projectile, the twist 
increases from the breech to a point about two calibres 
from the muzzle, and from this point to the muzzle it is 

166. Twist in Terms of Calibre — Kinds of Grooves. 

Twist in Calibres. — The twist is generally expressed in 
terms of the calibre, as one turn in ten calibres, etc. ; mean- 
ing that the projectile makes one complete turn in passing 
over a length of bore equal to ten calibres, etc. Suppose 
the groove to be developed (Fig. 163), and let a be the de- 
velopment of one turn of .the uniform groove, n the number 
of calibres in which the projectile makes one complete turn, 
and r the radius of the projectile, then the distance AB 
= 2nr and BC — 2nr, and 

2itr it 

tan = = — , 

2nr n 



for the value of the tangent of the angle of the rifling. For 
the increasing groove, <p is variable, but for any point, its 

value is -. In our service, the rifling of sea-coast guns is 

increasing, from one turn in 50 calibres at the breech, to 
one turn in 25 calibres at a distance of about two calibres 

from the muzzle. For the field-guns, the rifling was for- 
merly uniform, but in the later models an increasing twist 
has been adopted. 

Kinds of Grooves. — The number, depth, and width of 
grooves depend on the rotating device. By a groove is 
understood the spiral cut made in the bore, and by a land, 
the space between two adjacent grooves. 

When rifling was first introduced, the grooves were few 
in number, and as the points of contact of the projectile 
with the bore were also few, these points required consid- 
erable strength. The grooves were therefore made corre- 
spondingly deep and wide. This decreased the strength of 
the gun, as it increased the diameter of the bore subjected 
to the action of the powder-pressure. With a change in 
the rotating device, the grooves increased in number, and 
decreased in depth and width. This is called polygroove 
rifling, and adds greatly to the strength of the gun. In 
spite of this, the grooves are sources of weakness, as the 
action of the powder-gas tends to erode them at the junc- 
tion of lands and grooves, and all sharp corners must be 

In small arms the presence of grooves adds to the diffi- 
culty of cleaning the bore, and the grooves in these guns 
are made as shallow as possible. 


The shape of the groove in the sea-coast guns in our ser- 
vice is shown in Fig. 164, which gives the grooves of the 8" 

Fig. 164. 

The number of grooves in sea-coast guns, is six times the 
calibre of the gun in inches. Thus the 8-inch rifle has 48 
grooves and lands ; the 10-inch, 60, etc. 
167. Rotating Devices — Studded System — Flanged System. 

Rotating Devices. — The spiral grpoves having been cut 
in the bore of the gun, it is necessary to attach some device 
to the projectile which will fit into these grooves, and com- 
municate the required motion of rotation to it. Although 
muzzle-loading projectiles are practically obsolete, a few 
such guns still remain in our service, and a description of 
the means employed to give rotation to their projectiles 
will show the development of such devices. 

Since muzzle-loading projectiles are of less diameter 
than the bore, the rotating device must be made either to 
fit the grooves before firing, or to do so after firing, by the 
action of the powder-pressure. Accordingly, the rotating 
devices for muzzle-loading projectiles are divided into : 

1. The studded or flanged system. 

2. The expanding system. 

Studded Projectiles. — This system was generally used 
for muzzle-loading projectiles in Europe, and especially in 
England. The projectile (Fig. 165) was provided with studs 
made of a soft metal, such as zinc or copper, to, avoid 
wearing the lands of the rifling. These studs were arranged 
in two or three rows, depending on the length of the pro- 
jectile, and at an inclination equal to the angle tp of the 
grooves. They were inserted into undercut holes in the 
projectile, and subjected to pressure, by which the soft metal 
was forced to fill the holes. (See Fig. 165.) 



(D (l 


Fig. 165. 

The advantage of this system is that the projectiles are 
certain to take up the rifled motion. 
The disadvantages are : 

1. The projectiles must be adjusted to 
each particular twist ; and if two guns have 
the same calibre, but a different twist of rifling, 
different projectiles must be used for them. 

2. They cannot be used with an increasing 

3. Owing to the relatively small number 
of studs, the pressure upon each is great, and 
they are liable to shear. To avoid this they 
must be made strong, and this necessitates 
increased depth and width of rifling grooves, 
and a corresponding weakening of the gun. 

4. The stud-holes in the projectile weaken 
the latter, and their irregular surface increases the resistance 
of the air to its motion. 

5. Unless a gas-check is provided on the base of the pro- 
jectile, the escape of the gas between the projectile and the 
bore erodes the latter. 

The Flanged System. — In this system, flanges or ribs, 
fitting the grooves, were used instead of studs, the flanges 
being made generally of soft metal, except in case of the 
Whitworth. The principal example of this class is the 
Whitworth projectile, whose cross-section is a 
hexagon, and whose plane faces are inclined at an 
angle equal to that of the rifling (Fig. 166). The 
bore of the gun is rifled to correspond (Fig. 166a). 
In this case, the fit of the pro- 
jectile in the bore was very ac- 
curate, and any slight fouling 
interfered with the loading. As 
the flanges were of hard metal, 
they could not yield, and hence 
any obstruction was liable to 
Fig. 166. Fig. 166a. burst the gun These projec- 

tiles have given remarkable results as regards accuracy and 
penetration, but they are no longer used. 


168. Expanding System— Hotchkiss. 

Expanding System. — This system has been largely used 
in the United States for muzzle-loading projectiles. 

It consists in placing upon the rear end of the projectile, 
or upon its cylindrical body, a band of soft metal, such as 
lead or brass, which is expanded by the action of the pow- 
der-gas, and forced into the grooves when the gun is fired. 

The advantages of this system are : 

1. It may generally be used with either a uniform or an 
increasing twist. 

2. Projectiles of the same calibre, having different rotat- 
ing devices of this class, will fit any gun of that calibre, and 
are easily loaded. 

3. By the expansion of the rotating device the escape of 
gas between the projectile and bore is prevented, since the 
band acts as a gas-check. 

The disadvantages are : 

1. In some of the devices the gas was uncertain in its ac- 
tion, occasionally failing to produce expansion, and also tear- 
ing off the rotating device, or causing it to " strip ;" thus 
failing to give the rotary motion to the projectile, and when 
fired over the heads of friendly troops, causing accident to 
them from the fragments of the band. 

2. It was expensive, and required careful handling to 
prevent damage to the rotating device, and consequent ina- 
bility to load. 

3. It failed to centre the projectile in the bore. 
The principal examples of this class are : 

The Hotchkiss ; 
The Parrott ; 
The Eureka; 
The Butler. 

The Hotchkiss. — This projectile consists 
(Fig. 167) of a body, a ; a base, b ; and a jacket of 
lead, c, of the same diameter as the body of the 

When fired, the pressure of the gas forces the 
base*5 up on a, and thus the lead jacket c is ex- FlG - l6 7- 
panded into the grooves. 



169. Expanding System— Parrott— Eureka— Butler. 

Parrott. — In the Parrott system a brass ring or band, 
a, is cast upon the base of the projectile 
(Fig. 168), leaving a circular channel 
or groove, b, between the ring and 
the base. The gas acting in the chan- 
nel, forces the ring outward into the 
grooves. Frequently, however, the 
ring was torn off the base of the pro- 
jectile, as its hold was not sufficient. 

Eureka. — In this system a brass 
cup, a (Fig. 169), is placed on the base 
of the projectile. This base is made 
in the form of a frustum of a cone, 
with the smaller base to the rear. It 
has several longitudinal grooves, b, cut 
in it, into which corresponding projec- 
tions on the interior of the cup fit, and 
these prevent the rotation of the cup 
around the axis of the projectile, so 
that the rotary motion communicated 
to the cup by the rifling, is imparted 
to the projectile. The cup is curved 
where it rests against the rear end of 
the projectile, and to prevent stripping, 
it is held in place by the screw-bolt c. 
When the piece is fired, the gas-pressure 
forces the cup forward on the frustum 
of the base, till its curved surface rests 
against the rear of the projectile. 

This causes the sides of the cup 
to expand and forces them into the 
grooves. It is a very satisfactory muzzle-loading rotating 
device, and is still in use in our service. 

Butler. — This system was invented by Major Butler of 
the Ordnance Department, and consists (Fig. 170) of a brass 
ring a, having a lip or groove b in it. It is screwed to the 
base of the projectile to prevent stripping. When the piece 
is fired, the gas-pressure acts in the groove b, and forces the 




outer portion c of the ring outward into the grooves, and 
the inner portion d against the base of 
the projectile, thus insuring the adher- 
ence of the ring to the projectile. It is 
one of the best of these devices, and is 
still in service. a 

170. Breech-loading Projectiles— First Ro- 
tating Device — Hotchkiss Projectile 
— Copper Bands. 

Rotating Devices for Breech- 
loading Projectiles. — With breech- 
loading guns the powder-chamber is 
larger than the bore, and hence the 
projectile may have a rotating device 
larger than the bore, and this may be IG ' I7 °" 

compressed into the grooves by the action of the powder- 
gas. This is called the "compression system," to distin- 
guish it from the studded or flanged, and the expansion 
systems. Its advantages are : 

i. The projectile is certain to take the grooves, since its 
rotating device is compressed into them. 

2. The rotating device being larger than the bore before 
firing, it acts as a gas-check, and prevents any flow of gas 
between the projectile and the bore. 

3. It may be so shaped as to fit accurately the chamber 
of the gun before firing, and thus perfectly centre the pro- 
jectile, or make its axis coincide with that of the bore. 
This gives increased accuracy of fire, and it is impossible to 
accomplish it with any muzzle-loading system. 

Its only disadvantage is perhaps a slightly greater strain 
on the gun due to the increased pressure necessary to force 
the band into the grooves, but with the slow-burning powder 
used in modern guns this may be neglected. In fact it has 
been shown in Interior Ballistics that this increased resist- 
ance increases the muzzle velocit}'. 

First Rotating Device. — When breech-loading guns 
were first introduced, the rotating device was a jacket of 
lead (Fig. 171) cast on the body of the projectile. 



The objections to this are that it is difficult to make the 
lead adhere to the projectile, and it becomes / "^ 
detached in flight. This is dangerous in firing 
over friendly troops, and the energy commun- 
icated to this lead jacket is lost ; also the con- 
tact of the hot metal with the body of the pro- 
jectile in the process of casting, is apt to injure 
the structure of the latter. 

One rotating device of this class, the Hotch- 
kiss, is still in use for small-calibre projectiles. 

Hotchkiss B. L. Projectile. — The body 
of the projectile a, Fig. 172, is grooved cir- 
cumferentially for about one calibre in length, 

as shown, and 







cc 1 



-6 c/ 



<x I 


LJ / 





1- ( 
< ( 


Fig. 172. 

projections d of the band, and the metal thus 
displaced is forced into the grooves d ' . 

Copper Bands. — The lead jacket was next 
replaced by two bands of copper, Fig. 173, 
placed at equal distances from the centre 
of gravity of the projectile. The front band 
a, was used to support the forward por- 
tion of the projectile, and its diameter was 
slightly less than that of the bore between 
lands. The rear band b, was of a larger 
diameter, and was forced into the grooves, 
giving the rotation. 

Fig. 171. 
over these 
grooves c, is placed a band 
of brass, b. 

Longitudinal notches are 
also made in the grooves c, 
to prevent slipping of the 
band around the axis of the 

When the gun is fired, 
the gas compresses the band 
into the grooves on the 
body of the projectile, and 
it takes a corrugated shape. 
The lands cut through the 

Fig. 173. 



171. Rotating Device at Present — Profile of Band — Placing of Band 
— Position of Band. 

Recent Device. — It was found that the front bearing 
or supporting band was not necessary, and in modern pro- 
jectiles it is replaced by a slight swell, a, Fig. 174, at the 
base of the ogival head. The surface a is turned to a 
diameter slightly less than that of the lands, and the body 
of the projectile left as it comes from the casting or forg- 
ing process. 

This is less expensive, and leaves the metal on the exte- 
rior, which is stronger than any other part of the projectile. 

The rotating band is made of copper, fitted in an under- 
cut groove, as shown, Fig. 174. 

Fig. 174. 

Details of Rotating Band. — In modern guns, the 
powder-chamber is joined to the bore by a long conical 
slope, cd, Fig. 174. The exterior of the rotating band has 
a slope slightly greater than this, so that when the projec- 
tile is -in place, it will be accurately centred by the rear 
portion of the band, and this part of the band will also act 
as a gas-check, completely closing the interior of the bore. 
A number of grooves or cannelures, e, are turned on the 
exterior of the rotating band, to diminish the amount of 
metal to be cut through by the lands, allow space into which 
the portion cut out may be forced, and at the same time 
give the necessary length of bearing surface on the lands, 
by retaining the width of the band unchanged. The ex- 



terior diameter of the band at the rear, is slightly greater 
than that of the bore, measured from the bottom 
of the grooves. 

For the field projectiles, the band is more sim- 
ple, being a plain ring of copper with the front 
and rear faces bevelled, Fig. 175. 

Placing the Rotating Bands in Position. 
—This is generally done in our service, by ham- 
mering the band into place. The band may be 
made in two semicircles, or in a single piece of 
copper, whose length is just sufficient to en- FlG - J ?5' 

circle the projectile. In either case 
the cross-section before insertion is 
as in Fig. 176 at a. 

When inserted in the undercut 
groove b in the projectile, it is ham- 
mered, or subjected to pressure, till 
it takes the position shown at e, com. 
pletely filling the groove. 

It is then turned in the lathe to 
the proper dimensions. 

Position of Rear Band. — The 
position of the rotating band has 
great influence upon the range and accuracy of the pro- 
jectile, as has been shown by numerous experiments. It 
must be so placed that the distance cd, Fig. 176, will be 
sufficient to resist the shearing effect of the rifling, which 
would tend to strip the band off to the rear. This having 
been provided for, the best position of the band is deter- 
mined by experiment. 

172. Form of Projectiles — Head — Spherical Density — Weight. 

Form. — Numerous experiments have been made to de- 
termine the form of projectile that will best overcome the 
resistance of the air. 

The result of these experiments shows that the resist- 
ance is affected by the shape of that portion of the head 
where it joins the cylindrical body, and also by the rear 
of the projectile, since the shape of these surfaces affects 



the flow of the air along its sides. (See " Exterior Bal- 

Head. — The heads of all 
modern projectiles are ogival, 
the radius of the ogive being 
from 2 to 3 calibres. The more v^ 
pointed form gives less resist- 
ance, but introduces elements of 
weakness, and hence the above 
radii mark the limits thus far. 
The head is described with 
radii as shown in Fig. 177. 

Spherical Density. — Let 
W be the weight of a solid spherical projectile, whose 
radius is r, and W the weight of the oblong projectile of 
the same radius. 

The ratio 


s = ~w (250) 

is called the spherical density of the oblong projectile, and 
it measures the number of times the weight of the sphere 
is contained in that of the oblong projectile. We have 

W = $ nr'S, 

in which 8 is the weight of a cubic inch of the metal of the 
projectile, and r is in inches. Making S = £ lb., which is its 
approximate value, and taking n = 3, we have 

W=r s ; 

and substituting in (250), we have 


S = 


which is generally taken as the measure of spherical density. 

This value has increased from 2.0, when oblong projec- 
tiles were first introduced, to 3.0 in 1880, and 4.7 in 1894. 

Weight. — For the weight of a spherical projectile we 




or the weight of a spherical projectile in pounds is equal to 
the cube of its radius in inches. 

For an oblong projectile we have, equation (251), 

W = SX r\ 

or the weight of an oblong projectile in pounds is equal to 
its spherical density, multiplied by the cube of the radius 
in inches. Hence having the date of manufacture of a pro- 
jectile, its spherical density is known, and from this its 
weight. This rule gives very close approximations, and 
avoids the necessity of remembering anything except the 
spherical density. Since the weight is proportional to the 

cube of the calibre, the quotient — r will be constant for all 

similar projectiles. 

173. Manufacture of Projectiles — Pattern — Flask — Molding — Gate 
and Riser. 

Pattern. — Cast-iron projectiles are made as follows : 

A pattern is first made of the ^_ 1 

shape of the projectile to be cast. r~V 

Its diameter is slightly greater 
than that of the projectile, to 
allow for the shrinkage or con- 
traction of the metal in cooling. 
It is also slightly conical, instead 
of cylindrical, on the exterior, to 
permit its ready withdrawal from 
the mold. In Fig. 178 the pat- 
tern is made in two parts, and 
each part is conical from a to b. 
The spindle c is used to support 
the pattern in molding, and to 
mark the position of the core in 
the mold. 

It terminates in a conical 
bearing, d. Fig. 178. 

Core. — To form the interior cavity in a corea shot or 
shell, a second pattern or core e, Fig. 178, is required. This 



core is made of a mixture of sand and other substances 
which render it adhesive, and is formed upon a hollow 
spindle, f, which terminates in a conical bearing, g, of the 
same size as d on the shot-pattern spindle. The spindle/ 
being hollow, and having holes along it, allows the gases 
formed by the contact of the melted metal with the core, to 

Flask. — The pattern for the shot or shell is placed in a 
box called a flask, Fig. 179. This flask is made in parts 


Fig. 179. 

corresponding to the pattern of the projectile, and these 
parts are bolted together before casting. It contains a 
cross-bar, «, at the top, with a conical hole in it, into which 
the conical bearing of the spindle fits as shown. 

Molding.— To form the mold, the part of the pattern 
containing the conical spindle, is seated in the cross-bar a, 
and this part of the flask, with pattern, placed on a board, 


the plane xy down. Cylindrical sticks b and c are placed as 
shown, and molding composition, composed of sand, clay, 
and carbonaceous material, rammed in. This part of the 
flask is now inverted, the remainder of the pattern, the 
flask, and the cylindrical stick b put in place, and molding 
composition rammed in from the opposite direction, filling 
the flask. The parts of the flask are then separated along 
xy, and the pattern and sticks withdrawn. 

The core, having been separately molded, is then put in 
place, its spindle occupying the position shown, and being 
centred by the conical bearing in the cross-bar a. 

The parts of the flask are next bolted together. 

Gate and Riser. — The channel b is called the gate. 
The metal is poured through it into the mold. In large 
projectiles, it generally enters low down, and in a tangen- 
tial direction, to give a rotary motion to the metal as it 
enters the mold, and thus sweep the scoria and impurities 
to the centre and top. 

The channel c is called the riser. It allows the escape 
of gas from the mold, and the collection of the scoria, and 
also allows fresh metal poured in to fill up cavities and 
make up for shrinkage due to cooling. 

174. Operation of Casting — Kind of Iron Used — Position of Head 
and Base of Projectile in Mold — Steel Projectiles. 

Operation of Casting. — The cast iron is melted either 
in cupola or reverberatory furnaces, and run into ladles, 
from which it is poured through the gate b, into the mold. 
The pouring is continued till the metal fills the riser c, and 
fresh portions of melted metal are added to the riser as the 
latter sinks. 

As soon as the iron has cooled sufficiently, or set, the 
flask is removed, the core broken up, the spindle drawn out, 
and the projectile covered with the molding composition, to 
allow it to cool slowly. If a chilled projectile is to be cast, 
the chill is inserted in the mold before casting, as previously 

Kind of Iron. — For small projectiles, since they cool 
rapidly, and become very hard, soft iron is employed. For 


large projectiles, a harder and tougher iron is used. The 
selection of the proper kinds of iron can only be determined 
by experience, and it is usual to prescribe a certain tensile 
strength for each kind of projectile, and to test specimens 
from a number of them, to see that they come up to the re- 
quired standard. 

Position of Head and Base in Mold. — In Fig. 179 
the projectile is shown cast head down, with the core-spin- 
dle projecting through the base. This position gives great 
density to the head, and less to the base. For armor- 
piercing shot, and in all cases where great strength of head 
is required, the casting is made in this position. But for 
shell, especially those with a base fuze, it is important to 
have a strong and sound base, as if it is weak or spongy 
the gas from the powder-charge would penetrate the base, 
and burst the shell in the gun. In this case, therefore, the 
shell would be cast base down. 

Steel Projectiles. — Forged steel projectiles are cast 
as ingots, and are forged, and bored and turned to proper 

They are then tempered by a secret process, and are now 
made of such hardness and toughness, that they will pene- 
trate the best armor-plates whose thickness does not exceed 
i-J times their diameter, without cracking or deforming the 

Cast-steel projectiles are also tempered by a secret pro- 

175. Inspection and Proof of Projectiles — Quality of Metal — Shape 
and Dimensions — Eccentricity — Ballistic Test. 
The objects of inspection are : 

1. To test the quality of the metal ; 

2. To see that the shape and dimensions agree with those 
specified ; 

3. To see that the centre of gravity is on or near the 
longer axis of the projectile. 

Quality of Metal. — This is determined by testing spec- 
imens taken from different lots. For cast-iron projectiles, 
the soundness is tested by striking the projectile with a ham- 



mer, and a punch is used to determine the depth of any holes 
that may be discovered. Finally the shot or shell is sub- 
jected to water or steam pressure, applied to its interior. 
Any cracks or cavities will be detected by the escape of 
the water or steam. Chilled shot are struck with a hammer, 
at the junction of head and body. 

For Steel Shot and Shell chemical analyses are made, to 
determine the composition. After the final treatment, the 
shot are cooled to about 40 F., and then suddenly heated by 
plunging them into a water-bath, at a temperature of 212° F. 
When they become uniformly heated to this temperature, 
they are suddenly plunged, with their axes horizontal, half 
way into a bath of water, at a temperature of 40° F. Any 
great initial strain to which they may have been subjected in 
tempering, will be detected by this treatment. The shell 
are subjected to an interior hydraulic pressure of 1000 lbs. 
per square inch. 

Shape and Dimensions. — These are determined by tem- 
plets and gauges. For example, the profile of the projec- 
tile is determined by using a templet of sheet iron or steel, 
correctly made, and applying it to the exterior of the pro- 
jectile as in Fig. 180, a being the templet. 



Fig. 180. 

The diameters are determined by two rings, called ring 
gauges, Fig. 181. One of these has a diameter equal to 
the maximum that is allowed, and the other the mini- 

The maximum ring must pass over all the projectiles, and 
the minimum over none. 

Eccentricity. — When the centre of gravity of the pro- 



jectile does not lie on the longer axis, the projectile is ec- 

This eccentricity, if large, affects the 
flight of the projectile, causing irregu- 
larity, and hence its limits must not ex- 
ceed a certain amount. To detect it, 
the projectiles are first placed on a roll- 
ing-table, which is an iron table having 
two parallel ribs, a a, Figs. 182 and 183, 
at a distance apart slightly less than 'the 
length of the cylindrical body of the pro- 

This table being leveled, if the centre 
of gravity of the projectile, does not co- 
Fig. 182. incide with the longer axis, the projec- 
tile when rolled on the ribs, as shown, will come to rest 
with its centre of gravity below that axis. If no eccen- 
tricity exists, the projectile will remain indifferently 


■ ■ 







Fig. 183. 

in any position. When eccentricity is detected by this 
means, its amount can be measured with the eccentric cali- 
pers. These consist of a curved steel arm, d, Fig. 183, car- 


rying a sliding point, b, and a scale, c. The point is gradu- 
ated in inches, and c is a vernier scale. The thickness of 
wall is read off on the scale, and that of the opposite wall 
also. One half the difference of the readings, gives the 

Ballistic Test.— Steel shot and shell are subjected to 
actual firing tests against armor-plates. For this purpose a 
certain number are taken from each lot manufactured. The 
shot are fired with a striking velocity of 1625 feet-seconds 
against a steel plate i\ times the calibre of the gun in thick- 
ness, and the 12" mortar shell against a 4^-inch steel plate, 
at an angle of 60°. The shot and shell must penetrate com- 
pletely in each case, without breaking up. 


176. Kinds of Armor. 

Armor may be divided into — 

1. Chilled cast iron ; 

2. Compound ; 

3. Steel. 

Wrought-iron armor is now obsolete. 

Chilled Cast-iron Armor. — This armor, on account of its 
great weight, is used only on land, in the form of turrets. 

It is manufactured by Gruson, of Germany, and is cast 
in large blocks of the proper shape, the outer face of the 
blocks being chilled, and thus acquiring great hardness. 
These blocks are built into turrets, whose form is shown in 
the text-book of the Engineering course. It depends for its 
great resistance upon the following : 

1. Its intense surface hardness prevents the entrance of 
the projectile ; 

2. Its great mass distributes the effect of the blow ; 

3. Its curved form deflects the projectile. 

Its resistance to penetration is greater than that of any 
other armor. 

Compound Armor. — Wrought-iron armor was the first kind 
adopted, and it had sufficient resistance to' keep out the or- 
dinary cast-iron projectiles, but was readily penetrated by 
those of chilled cast iron. 


It became necessary, therefore, to harden the face ot the 
armor in order to break up these projectiles. This led to 
the introduction of the compound armor, which has been 
extensively used in England, and is still employed there. 

It is formed by welding a hard steel face to a wrought- 
iron back, and the armor is distinguished into two makes, 
according to the method of welding adopted. 

The two methods of manufacture are : 

i. Cammell & Co. — Wilson's Patent. — The firm of Cammell 
& Co. manufacture compound armor by the Wilson patent, 
which consists in forming a back of wrought iron, by forg- 
ing or rolling. This back is placed in a furnace, raised to a 
welding heat, and while at this temperature a layer of 
melted steel is run on one of its faces. After partially cool- 
ing, the compound plate is removed from the furnace and 
passed between heavy rolls, to reduce it to the proper thick- 
ness, ar.d improve its quality. The steel face is then treated 
to remove strains. 

2. Brown & Co. — Ellis Patent. — This method consists in 
forming the wrought-iron back and hard steel face sepa- 
rately. These are then placed in a furnace parallel to each 
other, and a short distance apart, and raised to a welding 
heat. Melted steel is then run between the plates, welding 
them together. 

177. Steel Armor — History — Improvements — Latest Steel Plates- 
Harvey and Tresidder Processes of Surface Hardening. 
History.— Steel armor, when first introduced, was hard 
and brittle, and broke up under the action of projectiles. 
The percentage of carbon was then reduced, and the plates 
no longer broke up, but allowed the projectiles to penetrate. 
It was shown, however, by the Italian experiments at Spez- 
zia in 1876, that the low steel plate was superior to those 
made ot wrought iron. To prevent the penetration of pro- 
jectiles, the face of the plate was tempered in oil, or oil- 
hardened, and the plate then annealed, to remove internal 
strains. As projectiles improved, however, this hardness 
was not great enough to resist penetration, and hence new 
improvements were made. 


Improvements. — These consist generally — 
i. In having better facilities for the mechanical treat- 
ment of steel in large masses, such as heavy hammers, 
forging-presses, etc. 

2. Combination of the steel with other ingredients, such 
as nickel, which increases its toughness and tenacity, and 
consequently decreases its tendency to break up. 

3. Special treatment of the steel, as the Harvey process, 
by which the face is made hard, while the back retains its 

Latest Steel Plates. — From the time of the Italian 
experiments in 1876, up to those at Annapolis in 1890, com- 
petitive trials have been going on between the steel and the 
compound armor. 

The tests at the latter place, showed the superiority of 
the all-steel plate, and it has been adopted in our Navy. 

The steel plates which have given the best results up to 
the present time, are known as high-carbon nickeled steel 
and low-carbon nickeled steel, referring to the relative quan- 
tity of carbon in the alloy, although it is small in each case. 
The high-carbon nickeled*steel plate has so far given the best 
results. All the plates are hardened on the surface by the 
Harvey process. 

Harvey Process. — This consists in carbonizing to a 
higher degree the outer surface of the plate, for a certain 
depth, depending on the dimensions of the plate, and then 
hardening this surface. 

The process is as follows : The plate is embedded in 
sand and clay in a furnace, leaving a certain thickness ex- 
posed. The furnace is then filled with carbonaceous material, 
well packed over the exposed portion of the plate, and the 
whole raised to a high temperature, which is maintained for 
some time. The material is then removed, and when the 
plate has cooled sufficiently, its surface is hardened by the 
application of cold water. 

Tresidder Process. — This process is used in England, 
and consists in heating the plate to a certain temperature, 
and applying cold water to the surface under heavv press- 
ure, and through a number of small holes, thus producing 



numerous small streams of water acting together. The idea 
is that the force with which the water is applied, brings it 
directly into contact with the hot metal, thus cooling it 
rapidly, and preventing the formation of the envelope of 
steam (spheroidal state) around the particles of water, and 
the consequent slow rate of cooling, which would be the 
case if the water were applied without pressure. 

178. Effect of Projectiles on Armor — Early Armor — Compound 
Armor — Steel Armor. 

Armor yields in two ways : 

i. By racking, or breaking up ; 
2. By punching. 

Early Armor — Punching. — Wrought-iron armor was at 
first generally attacked by heavy projectiles, moving with 
low velocities, as with the old 15-inch smooth-bore. Al- 
though the armor itself was soft, and yielded naturally by 
punching, the effect of these projectiles was to break its 
fastenings, and cause it to rack. As guns and projectiles in- 
creased in power, however, this armor yielded entirely by 
punching. That is, the effect of the blow was to punch a 
hole through the armor, and if the bolts held, no part of 
the plate beyond that struck, was affected. 

Racking. — The object of armor, however, being to keep 
'out projectiles, this defect led to the introduction of the 
harder kinds, as shown. This hard armor, instead of yield- 
ing locally to the blow of the projectile, distributed the 
energy of that blow over a greater mass of the plate, and 
when the energy was sufficient, the plate broke up, or was 

Compound Armor. — The effect of projectiles upon this 
armor, is to break up the hard steel face, and to punch the 
■wrought-iron back. The punching effect is, however, very 
much diminished by the energy lost in breaking up the 
steel face. The difficulty with this armor seems to be that 
the welding of the steel face to the wrought-iron back is 
uncertain, and hence after a few blows, the steel face breaks 
up, and separates from the wrought-iron back. Also the 
face being elastic, and the back having no elasticity, the 


former, after being struck, tends to recover its first position, 
While the latter does not. This increases the tendency of 
the front and back to separate. It follows that a compound 
plate must have a rigid support in rear for the best results. 

Steel Armor. — This armor at first yielded by rack- 
ing, owing to its hardness and brittleness. Oil-hardening, 
however, decreased its brittleness and increased its tough- 
ness, so that the effect of the improved projectile was to 
punch it. 

The modern processes of surface-hardening, however, 
have combined hardness with toughness, so that, at the pres- 
ent day, the armor resists both racking and punching to a 
remarkable degree. The history of the improvement is ob- 
vious : decrease of hardness and brittleness to decrease 
racking, and afterwards a combination of hardness and 
toughness to prevent both punching and racking. 

179. Backing — Fastenings for Old Armor. 

Backing. — That portion of an armored structure di- 
rectly in rear of the plate, is called the backing, and the 
character of this backing depends upon that of the armor. 

Chilled Cast Iron. — This armor has no backing, or rather 
the cast iron itself may be regarded as forming the backing 
for the hard chilled face, since the thickness and mass are 

Compound Armor. — For this armor, a rigid backing is re- 
quired, to give the best results. For land structures, a rigid 
backing may be used, since weight is no objection, but for 
ships, such a backing is impossible, and it would therefore 
seem that this armor cannot give the best results when used 
under such circumstances. It is, however, the standard 
armor of the British Navy. An objection to the rigid back- 
ing is that it tends to cause racking of the armor-bolts. 
When an elastic backing is used with this armor, it allows 
the plate as a whole to yield to the blow of the projectile. 
But, as before stated, the steel face, being elastic, returns to 
its former position after the blow, while the wrOught-iron 
back does not, and hence there is a tendency for the face 
and back to separate. The rigid backing, on the other hand, 
has the opposite effect. 



Steel Armor. — This armor, being elastic, requires an elastic 
backing, and not a rigid one, since the elastic backing allows 
the plate to yield to the force of the blow, and the elasticity 
of the plate causes it to return to its former position. 

Fig. 184 shows the arrange- 
ment of backing as generally 
used, and may consist of one or 
two thicknesses of timber, b, 
placed against the steel sides, 
a a, of the vessel. 

Fastenings for Old Ar- 
mor. — The original armor-bolt 

Fig. 185. 

Fig. 184. 

Fig. 186. 

for wrought-iron armor, was shaped as shown in Fig. 185. 
The objections to this bolt were : 

1. If under water, it leaked. 

2. When the plate was struck, the bolt would snap at 
the bottom screw-thread a, and the nut would fly off, acting 
as a projectile. 

The French made the first attempt to remedy this, by 
using an ordinary wood-screw, Fig. 186, which screwed into 
the backing, but did not pass completely through it. This 
prevented leakage, and the flying of the bolt-heads about 
the deck. 

The English changed the arrangement of the armor-bolt 



by placing a rubber washer, k, under the nut, and cutting a 
plus thread on the bolt, as in Fig. 187. In this case the bolt 

Fig. 187. 
has the same strength throughout, the thread is not a source 
of weakness, and the rubber washer allows a certain play in 
the direction of the length, and thus prevents snapping from 
the sudden strain, and it also prevents leaking. 

180. Improved Fastenings for Iron Armor — For Steel Armor — 
Tests of Armor-plates. 
IRON ARMOR. — In addition to the strains brought to bear 
upon the bolt in the direction of its length, causing elonga- 
tion and snapping in the older 
forms, there is a cross-strain due to 
the displacement of the armor side- 
ways. To obviate this, the English 
spherical-headed bolt was devised, 
as shown in Fig. 188. This shape of 
head and nut, causes the strain to be 
always along the axis of the bolt ; and to allow the bolt to 
take its normal position when the plate is displaced laterally, 
a clearance is made around it. 

Steel Armor. — With this armor, or with the compound 
armor, where it is necessary to preserve the steel or hard- 
ened face intact, the bolt must not pass through the plate. 
It is therefore screwed for a short distance into the back of 
the plate. In naval vessels, the backing is comparatively 
thin, and hence the bolt must be lengthened by some 
means, so that the stretch per unit of length may not be 
sufficient to break the bolt. The following arrangement is 
adopted in the Navy (Fig. 189). 

Fig. i 



a is the armor-plate ; b, the backing ; c, the armor- 
bolt, reduced in diameter as shown, to give lateral play- 
in the iron pipe d, which passes through the backing 
and furnishes a seat, for the bolt ; e and /, rubber wash- 
ers which are set up by the pressure of the nut g, and 
prevent leaking ; h, a sleeve, whose object is to increase the 
length of the bolt, so that the elongation per unit length 

Fig. 189. 

when the plate is struck, may prevent fracture ; j, a. cup- 
shaped washer, containing the rubber washer k, and the 
iron washer /. The washer k gives elasticity to the whole 
system. The sleeve h distributes the pressure of the nut g 
over a large area of the sides of the ship, and also, as stated, 
increases the length of the bolt. The number of bolts is 
greater for the steel and compound armor, than for the old 
wrought-iron armor. 

Tests of Armor-plates. — The test of armor-plate pre- 
scribed by the Ordnance Department is as follows : One 
plate is selected from a lot, and is bolted to an oak backing 
36 inches thick, properly supported, with rubber washers 
placed between the steel washers of the bolts in rear. The 
calibre of the gun is to that of the plate as 1 : \\ ; that is, 
for a 9-inch plate an 8-inch gun, etc. One armor-piercing 
shot is fired from this gun, so that the centre of the shot-hole 
shall not be nearer any edge of the plate than i\ calibres. 

The projectile must have the following striking-energy : 

For an 8-inch gun 3000 foot-tons 

For a 10-inch gun 5000 " 

For a 1 2-inch gun 7643 " 


Under these conditions, the whole of the projectile must 
not get through the plate, nor must the plate break up, or 
pieces be detached, or cracks produced which expose the 
backing to view. 

181. Penetration of Armor — Wrought Iron — Steel. 

Wrought Iron. — Most of the formulas for penetration 
have been deduced for wrought-iron armor, on account of 
the length of time it has been in use, and the numerous ex- 
periments that have been made upon it. 

In deducing these formulas two different hypotheses 
have been adopted : 

1. That the projectile acted as a punch, separating a 

-disk of metal from the plate. In this case, the resistance to 

be overcome, was the resistance of the metal to shearing 

along the circumference of this disk, and hence the energy 

of the projectile to overcome this resistance was estimated 

per inch of shot's circumference, and was obtained by di- 

viding the total energy by the circumference, or — . 

2. That the projectile acted as a wedge, forcing the par- 
ticles of the metal apart. In this case the penetration is 
proportional to the energy per unit of area of cross-section, 


•or — 

n T 

The principal formulas deduced under the first hypothe- 

esis are : 

f — ——; (Fairbairn's) . . . (252) 


f*% = g6 , , ; (English Admiralty) (253) 

fM = ixd i (Muggiano) . . . (254) 

And under the second hypothesis : 

^=T*&^ ; (deMarre's) . . . (255) 


t— -?—.£— o.i^d;, (Maitland's) . . . (256) 
608.3 V » 

"=dW. ; < K ™pp' s » • • • • < 2 "> 
'•■=J£ms- < G4 ™> < 2!8 > 

In these formulas 

t is the thickness of wrought iron, in inches, which 
the projectile will penetrate ; 
E, the energy of the projectile in foot-tons ; 
d, its diameter in inches ; 
p, its weight in pounds ; 
v, its striking velocity in feet-seconds ; 
k, a constant. 
Steel Armor. — For steel armor, it was customary to 
calculate the penetration in a wrought-iron plate of the 
same thickness, and add a certain percentage of increase of 
resistance, varying from 10 to 30 per cent. This method is 
not satisfactory, as steel armor varies greatly in resistance 
according to treatment ; and for the modern Harveyized' 
plates, penetration seldom occurs, owing to the hard face,, 
unless the gun greatly overmatches the plate. 

The formulas generally used are those of de Marre, as 
follows : 

For soft plates of Creusot steel, backed, 

r' = 0.0009787^. (259). 

For the steel plates used as protection against steel shell 
from rapid-fire guns, unbacked, 

?■> = 0.000734^ (260). 

For the wood backing, with plate in front of it, 

r- 6 = 0.006168^- ( 2 6i> 


Captain Orde Browne gives a rule which enables some 
idea to be formed of the relative powers of guns against 
armor, as follows : The penetration of a projectile in wrought- 
iron armor is one calibre for every thousand feet striking vel- 

For example, a io-inch projectile, striking with a velocity 
of 1200 feet-seconds, will penetrate 1.2 calibres, or 12 inches. 




182. Definition — Classification — Time Fuzes — Requisites — Difficul- 

Definition. — Fuzes are the means used to ignite the 
bursting charge of a projectile at any point of its flight, or 
upon impact. 

Classification. — They are classified according to their 
mode of action, into — 

1. Time; 

2. Percussion ; 

3. Combination; 

4. Delayed action fuzes. 

Time Fuzes. — A time fuze is one which ignites the burst- 
ing charge at some fixed time after the projectile has left 
the muzzle, and it consists generally of a column of compo- 
sition, whose rate of burning is known, which is set on fire 
by the discharge of the piece, and whose time of burning is 
regulated by the length of the column. 

Requisites. — The requisites of a good time fuze are : 

1. Its rate of burning should be uniform, and not affected 
by storage or changes of climate. 

2. It must be safe in handling, and certain in its operation. 
These conditions are very difficult to fulfil, and hence a 

good time fuze is perhaps the most difficult one to obtain. 

Recent improvements have, however, done much to 
obviate the difficulties formerly experienced. 

Difficulties. — The difficulties in making a reliable 
time fuze are : 



1. To obtain a column of composition whose rate of burn- 
ing is uniform. 

The rate of burning of a composition depends upon its 
density, trituration, composition, and degree of moisture, as 
explained in Interior Ballistics. For the same composition, 
it is very difficult to obtain a uniform density throughout a . 
long column. The old method of preparing a time-fuze was 
to place a small quantity of the composition in the fuze-case, 
and strike it a certain number of blows with a mallet and 
drift, and repeat this operation till the fuze was completed,.. 
This did not give uniform density. 

A second method was to subject it to hydraulic-pressure, 
but this also failed. The method now in use gives better 
results, and will be explained. 

2. For long times of burning, a long column of composi- 
tion is required, and the results obtained by the old method 
were so unsatisfactory, that the ingredients of the composi- 
tion were varied, in order to give a decreased rate of burn- 
ing and thus shorten the column. This changed irregularly 
the rate of burning, increased the difficulty of preservation, 
and, also increased the residue. 

3. It was found impossible to guard against the changes, 
dus to storage, climate, etc., as they affected both the 
composition, and the fuze-case. 

4. After a uniform rate of burning is obtained, the press-. 
ur,e of the air on the composition, during flight, changes 
this rate. 

5. With modern breech-loading guns, and high veloci- 
ties, a small error in burning, increases the error in burst- 
ing of the projectile. 

6. The flame from the powder-charge will no longer, 
ignite the fuze. 

183. Time Fuzes — Difficulties, How Overcome. 

To overcome these difficulties, the following changes in 
manufacture have been made : 

Uniform Rate of Burning. — To obtain a uniform rate of 
burning, and a column of composition of sufficient length to 
answer for, the greatly increased ranges, a, lead tube 0.62 


inch in diameter is filled with mealed powder. The ends 
are then closed, and the tube, with the enclosed powder, 
drawn out by a process similar to that of wire-drawing, till 
the diameter .is decreased to 0.152 inch. The rate of 
burning is tested by burning inch lengths of this compressed 
powder, and its rate is found to be very uniform. In this 
case, the pressure is applied in the direction of the shortest 
dimension of the column, so that it is more uniform in its 
effect ; and if there be any difference in density, this differ- 
ence, is neutralized by the burning of the column at right 
angles to the direction of the pressure, so that the same 
variation of density exists throughout each cross-section. 

Changes of Climate, etc. — These have less effe'ct upon the 
composition, because it is contained in a metallic case which 
is less subject to change. 

Variation due to Pressure of Air in Flight. — This is cor- 
rected for, as far as possible, by graduating the fuze tempo- 
rarily with the rate of burning as determined at rest, and 
then correcting this graduation, by actual test, on the firing- 

Ignition of Fuze. — With the old fuzes, and muzzle-loading 
projectiles, there was always a space between the surface of 
the bore and that of the projectile, through which the flame 
from the powder-charge could pass to ignite the fuze. This 
was called the " windage." With modern breech-loading 
projectiles, this space is closed by the band of the. projectile, 
and hence the flame cannot pass through to ignite the fuze. 
The arrangement for accomplishing this with the modern 
time fuze, will be explained. 

184. Older Forms of Time Fuze in Use — Mortar Fuze — Sea-coast 
Fuze — Bormanu Fuze. 
The older forms of time fuze still in use in the U. S. 
service are : 

The mortar-fuze ; 
The sea-coast fuze ; 
The Bormann fuze. 

Mortar Fuze.— This is used in the old siege and sea- 



coast smooth-bore mortars. It consists (Fig. 190) of a coni- 
cal case or plug, a, of wood graduated on 
the exterior into inches and tenths. On the 
interior there is a cylindrical cavity, b, bored 
out nearly to the bottom, and filled with the 
fuze-composition, driven as explained. The 
top of this cavity is enlarged at c, and filled 
with mealed powder moistened with alcohol, 
to insure ignition from the flame of the 
powder-charge. This is covered with a 
paper cap, c', on which is marked the rate 
of burning in seconds per inch. The gradu- 
ations begin at d, and stop at e. To prepare 
this fuze for use, the paper cap is removed, 
the fuze cut at the proper division, counting 
from the top, by sawing off the lower end, or 
better by boring a hole into the composition 
with a gimlet, as at/", as this prevents the composition from 
being dislodged by the shock of discharge, and finally by 
driving with a drift the fuze into the fuze-hole of the shell. 

The Sea-coast Fuze. — This was used in the old smooth- 
bore guns, and at present in the 15-inch Rodman gun. 

For ordinary firing, this fuze (Fig. 191) is composed of a 

Fig. igo. 


Fig. 191. 

conical wood plug, a, with a conical hole, b. In this hole is 
placed the fuze, c, which is contained in a conical paper case. 



The fuzesare of variable composition, and are marked.on. 
the exterior according to their time of burning. For ricochet 
firing over water, and for heavy charges, a. brass f iize-plug* 
d, of the same shape is used, the distinctive feature being 
the water-cap, e, which is a brass cap, having a zigzag chan- 
nel, filled with mealed powder. The shape of this channel 
renders the access of water difficult, and hence prevents the 
extinction of the composition. 

The Bormann Fuze. — This was used with spherical 
shell and shrapnel, in the field service. 

It consists (Fig. 192) of a pewter fuze-case, a, containing 
a ring of composition, b. Over this ring, b, lies an arc, c, 
graduated in seconds. At the zero end of the arc, this ring, 


Fig. 192. 

b, communicates with a channel, d, filled with fine powder, 
leading into a chamber, e, filled with the same powder, 
which is supported by a tin disk, f. The composition, b, is 
pressed into its recess in the direction of its shortest dimen- 
sion, and burns around the ring at right angles to this direc- 
tion. Hence the fuze possesses one of the good qualities of 
the modern time-fuze. The other end of the ring of com- 
position, has no communication with the chamber e. Owing 
to its shape, and the material of which the case is made, this 
fuze is liable to be driven into the shell by the shock of dis- 
charge ; and to prevent this, and increase the effect of the 
bursting-charge in the projectile, a wrought-iron disk, g, is 
screwed into the fuze-hole, below the fuze. 

The action of the fuze is as follows : If required to burn 
any given time, say four seconds, the case, is cut at; the mark 
4, exposing the ring of composition. 


This composition then burns in both directions ; but hav- 
ing no communication with the chamber e, in the direction 
toward 5, it will burn for four seconds, and then fire the 

The objections to the fuze are : 

1. Its time of burning is too short for modern ranges ; 

2. It is difficult to ignite by the flame from the charge ; 

3. If once cut, it cannot be used for a greater time of flight. 
The modern time fuze is not used, except in combination 

with the percussion fuze. 

185. Percussion Fuzes — Requisites — Essential Farts. 

A percussion fuze is one which is prepared for action by 
the shock of discharge, and which acts by the impact of the 

Requisites. — The requisites of a good percussion fuze 
are, that it shall be safe in handling, and certain in its opera- 

Safety in Handling. — This requires : 

1. A safety device which will prevent accidental dis- 
charge in store, transportation and handling, or from acci- 
dental shock, such as dropping the projectile. 

2. A safety device which will prevent accidental dis- 
charge in loading, and which will be released only on firing 
the piece. 

These may be combined in one, as will be seen later. 
Certainty of Action. — This requires : 

1. That all the parts of the fuze be protected from clog- 
ging, by the action of the bursting-charge in transportation, 
and by other causes, such as dust, etc. 

2. A safety device which will prevent relative motion of 
the parts of the fuze during flight. 

Essential Parts. — The essential parts of every percus- 
sion fuze are : 

A case, to contain all the moving parts and protect them ; 

A plunger, which is moved backward or forward on im- 
pact, and which fires the fulminating composition ; 

A fulminating composition, which is fired by the impact 
of the plunger; 


The priming, which is a charge of powder ignited by the 
fulminate, and which ignites the bursting-charge; 
A safety device in transportation ; 
A safety device in loading ; 
A safety device in flight. 

186. Percussion Fuzes in TT. S. Service — Classification — Hotchkiss 
Front Percussion Fuze — Action of Fuze — Safety Devices. 

Classification. — Percussion fuzes are classed accord- 
ing to the position they occupy in the projectile, as: 

i. Front fuzes, which are inserted in the head of the pro- 
jectile, at the point of the ogive ; 

2. Base fuzes, which are inserted in the centre of the base. 

The front-fuze is sometimes used with field projectiles, 
and generally when penetration is not required. 

The base fuzes are used with armor-piercing projectiles, 
and generally where penetration is required, and where the 
head of the projectile must have great resistance. 

The front fuze has the advantage of having the bursting 
charge of the projectile thrown toward it on impact, and 
there is no danger of the flame from the charge in the gun 
entering the cavity of the projectile, and causing premature 

The percussion fuzes used in the U. S. service are the 
Hotchkiss Front and Hotchkiss Base Fuzes, or modifica- 
tions of them. 

Hotchkiss Front Percussion Fuze. — This fuze con- 
sists of a brass case, «, Fig. 193, threaded on the exterior for 
screwing into the projectile. The upper end is closed by a 
screw cap, b, carrying a projecting point, c. In the case a, is 
a plunger, d, composed of a brass case, e, and a lead body, /, 
in which is a brass wire, g. The central part of the lead 
body carries the priming charge of powder, h, and on the. 
top of this priming is the fulminate, i. The brass case e, 
encloses the lead body /, to prevent the upsetting laterally 
of the plunger, by the shock of discharge, and its conse- 
quent wedging in the fuze-case. 

When the plunger is inserted in the case a, the brass 
wires g, occupy the position shown, and the rear end of a is 



closed by a conical lead plug, j, bearing against the 

Action of Fuze. — When the piece is fired, the shock of 
discharge causes the lead plug/ to be dislodged from its 
seat in the fuze, and to fall into the cavity of the projectile. 
The plunger d then moves to the rear, and rests, during 
flight, upon the shoulder k, at the bottom of the fuze cavity. 
Upon impact, the plunger d is thrown forward, the fulmi- 
nate i, striking the point c, and thus firing the priming 
charge h, which fires the bursting charge. 

Safety Devices in Transportation and Loading. — 
These are combined in this fuze, and are formed by the 
conical lead plug, bearing on the brass wire g. 

Safety Device in Flight. — In all percussion-fuzes, the 
plunger has a tendency to move forward in the fuze cavity 
during flight. This is due to the fact that the projectile is 
retarded by the resistance of the air, while the plunger, not 
being subjected to this action, is not affected by it, and its 
only retarding force is friction, which is very small. If the 
plunger moves forward, it will either explode the fulminate 
during flight, or else if the sensitiveness of the fulminate be 
diminished to prevent this, it will be so close to the point c, on 
impact, that it may not acquire energy sufficient to cause 
the explosion at that time. In this fuze, the safety device 
in flight, is provided by the wires g, which spread out- 


Ward 'When the lead plug _/' is dislodged, and thus prevent 
the forward motion of the plunger till impact. 

187. Hotchkiss Base Percussion Fuze — Action of Fuze — Safety 
Hotchkiss Base Percussion Fuse. — The Hotchkiss 
base percussion fuze consists of a brass case, a, Fig. 194, 

Fig. 194. 

of the shape shown. It is threaded on the exterior at b, 
for screwing into the projectile, and on the interior at c, 
for the cap, which carries the fulminate. The flanges at d 
are made thin, to act as a gasrcheck, and prevent the en- 
trance of the gas from the charge of the gun into the fuze- 
cavity, thus prematurely exploding the projectile. 

In the case a is a plunger, e, composed of a brass jacket, 
/, a lead body, g, and a firing-pin, h. The combination of 
lead and brass is for the purpose previously described. The 
firing-pin, h, is made of steel, roughened on the outside, and 
the lead body is cast around it, so that before firing its point 
is slightly below the upper surface of the plunger. 

The upper part of the fuze-case carries the screw cap i, 
which is composed of the party, which screws into the fuze- 
case, the fulminate k, the screw cap / closing j, and the 
safety disk of copper m. 

Action of the Fuze. — When the piece is fired, the 
shock of discharge causes the heavy plunger e to slide to the 
rear along the pin h, taking the position shown in Fig. 195. 




The action of the brass casing of the plunger is to 
prevent the spreading of the lead body, and consequently 
cause the latter to take a firm hold on the 

When the projectile strikes, the plun- 
ger is thrown forward, the point of the 
firing-pin passing through the hole n in 
the screw cap, strikes and explodes the 
fulminate, the flame from which passes 
through the hole o into the interior of the 
projectile, and ignites the bursting-charge. 
Safety Devices in Transportation 
AND Loading. — These are combined in 
this fuze and consist of : FlG - *95- 

i. The projecting pin h being held firmly in the lead 
body of the plunger, with its point below the upper surface 
of the latter, so that it requires the shock of discharge to 
force the plunger down over the pin, and allow its point 
to project. 

2. Making the lengths of the plunger and projecting 
portion of the pin h such, that before firing they are held 
tightly in position in the case, and hence the plunger cannot 
acquire any motion which might force it along the pin. 

Safety Device in Flight. — This is provided by the 
copper disk m on the bottom of the fulminate cap, so that 
if the point of the pin should touch the cap in flight, it will 
not cause an explosion. 

188. Combination Fuzes — Requisites — Frankford Arsenal Com- 
bination Fuze — Action of Fuze. 

A combination fuze is one which contains both a time- 
and a percussion fuze in the same case, and is intended to 
increase the chances of bursting the projectile, and of readil y 
and quickly varying the kind of fire. 

Requisites. — A good combination fuze must combine 
the requisites of both time and percussion fuzes, without 
being too bulky or too expensive. 

The Frankford Arsenal Combination Fuze. — This, 
fuze is used in the U. S. service for field shrapnel, and con- 
sists (Fig. 196) of a case, a, of bronze, the front portion of 


which carries the time fuze, and the rear portion the per- 
■cussion fuze. 

The time fuze is composed of the plunger b, the firing. 

Fig. 196. 

pin c, the cone d, the time-train e, the cover /, cap g, and 
clamping-nut h. 

The plunger b is cylindrical in shape, and contains the 
fulminate i, in a recess at its base. Its upper 
extremity is pierced to receive a safety-pin,/, 
■^ and there are five radial lugs, k, Fig. 197, which 
support the plunger on the top of the fuze 
body, and prevent it from falling against the 
firing-pin c, when the safety - pin at / is re- 
moved, before loading. 

The firing-pin c is of steel, inserted into the 
body of the fuze at the bottom of the plunger 

The cone d is an alloy of soft metal, held in 
place on the fuze-body by the clamping-nut h, and a groove 


m at the bottom, and is prevented' from turning by a steel 
pin, /. 

The lip m on the bottom of the cone, entering the 
groove in the body, acts as a gas-check to prevent ignition 
of the powder in the tube n. On the exterior of the cone d, 
is a left-handed groove which carries the time-train e, and 
this time-train communicates at its, lower end with the 
priming-charge in the tuberc, and thence with the chambers. 

The time-train e is formed, as previously described, of a 
lead tube, filled with mealed powder, and wire-drawn. 

The cover/is of brass, and is held in place by the cap g, 
and prevented from turning by a small pin projecting from 
the body a, and fitting in a slot in its lower edge. On the 
exterior of the cover is a left-handed groove, corresponding 
to that on the time-cone d, and this groove is pierced with 
holes numbered from i to 15, corresponding to the number 
of seconds, the spaces between the holes being divided into 
five equal parts. 

The percussion fuze is a modification of the Hotchkiss 
base fuze previously described, and consists of the primer 
in front ; a plunger-spindle, u, carrying a firing-pin, u'; a 
plunger-sleeve, v; a safety -ring of brass, w\ and a safety- 
disk of copper, t ; the fuze being closed in rear by the screw- 
plug 5, and this screw-plug, and the exterior of the plunger 
sleeve v, being grooved longitudinally, for the passage of 
the flame from the chamber to the bursting-charge. 

Action of Fuse. — 1. As Time Fuze. — Suppose the fuze 
is to burn 12 seconds. A hole is punched through the 
cover, time-train, and cone, into the interior of the fuze, at 
the 12-seconds mark. Just before loading, the safety pin is 
removed from the holey'. This allows the time plunger b to 
rest on the top of the fuze-body, where it is held by the five 
radial lugs, k. The projectile is now inserted in the gun. 
By the shock of discharge these five lugs are broken, and the 
time-plunger b is thrown to the rear, its primer striking the 
firing-pin c, which explodes the fulminate. The flame from 
the fulminate passes through the four radial holes p, at the 
base of the fuze body, and ignites the ring of compressed 
powder q. The flame from this powder, ignites the fuze 


composition at the hole marked 12, which has been punched 
through the time-cone d, and after burning for twelve sec- 
onds, this ignites the priming charge in the tube n and 
chamber o. The flame from this charge passes down along 
grooves r in the percussion fuze body and screw s, and 
ignites the charge. 

2. As a Percussion Fuze. — When the piece is fired, the 
plunger sleeve v slides relatively to the rear, against the 
resistance of the safety ring w, and this ring is pushed from. 
its groove, and along the spindle u. When the plunger 
sleeve v reaches its extreme rear position, the safety ring w 
slips into the groove w', and, as its diameter has been in- 
creased by passing over the plunger spindle, it now fits into 
the groove in the plunger sleeve, and locks the spindle and 
sleeve together. The point of the firing-pin u' now pro- 
jects beyond the plunger sleeve, and on impact, the sleeve 
and spindle are thrown forward, exploding the primer. 

Safety Device in Transportation. — The safety pin/, for the 
time-fuze, and the plunger sleeve v, and safety ring w, for 
the percussion fuze. 

Safety Device in Loading. — The radial lugs k for the time 
fuze, and the sleeve and ring, as before, for the percussion 

Safety Device in Flight: Percussion Fuse. — The copper 
disk t. 

189. Delayed-action Fuzes — The Merriam Delayed-action Faze — 
Action of Fuze. 

A delayed-action fuze is one which is prepared for action 
by the shock of discharge, and whose final action is retarded 
till the projectile has passed through the object or reached 
a certain position where its explosion will be most effective. 

The Merriam Delayed-action Fuze. — The principles 
of this class of fuzes will be best explained by the descrip- 
tion of one of them which has been tried — the Merriam Fuze. 

This fuze consists of a case ®r body, a, Fig. 198,' 
threaded on the exterior for screwing into the base of 
the projectile. In the interior of the case are a ham- 
mer, b, in the form of a sphere, held in place by 



clips, c, which abut against a shoulder in the case and a 
■circular recess in the ball b ; 
two pistons, d, which are 
forced forward by the press- 
ure of the gas of the powder- 
charge in the gun ; a flat 
spring, e, which keeps the ball 
in place during flight ; three 
small balls, /, which are held 
firmly in their seats below 
three percussion-caps, g; a 
valve, h, in front, which 
moves parallel to the axis of 
the fuze, and carries on its 
forward face a ring, i, of com- 
pressed powder ; four radial 
chambers, j, carrying priming-charges of powder, and a 
screw, k, whose use will be explained. 

Action of Fuze. — When the piece is fired, the pressure 
of the gas pushes forward the two pistons d, and these, 
striking the clips c, push them off the shoulders in the case. 
The ball b, is thus left free to move forward, but is pre- 
vented from doing so in flight, by the flat spring e. When 
the projectile strikes the object, such as an armor-plate, the 
ball b is thrown forward, and, striking one of the small balls 
f, drives it against its percussion-cap, exploding it. The 
flame from this cap passes into the chamber /. 

When the ball b is thrown forward by the striking of the 
projectile, the valve h also moves forward at the same time, 
and bears against the front of the fuze-case, thus closing the 
openings 00 which communicate with the priming-charges 
in the chambers/ The valve h reaches its seat against the 
front of the case before the ball b explodes the caps g, be- 
cause it has a shorter distance to travel. The flame from 
the percussion-caps, entering the chamber /.ignites the com- 
pressed powder ring i, but, as this ring of powder is held 
■between two closely-fitting surfaces, it can burn only on 
the edge. As long as the projectile is passing through the 
plate, or until it stops in the plate, it is being retarded, and 


the acquired energy of the valve will keep it in contact with 
the front face of the fuse. As soon, however, as the projec- 
tile passes through the plate, or stops in it, the valve h will 
move back and open the holes o o, and the charge will be 
fired. The screw k, holds back the valve h, when screwed 
down, and there is no delayed action in this case. 


190. Definition — Classification — Requisites — Common Friction- 
Primer — Action. 

Definition. — Primers are the means employed to ignite 
the powder-charge in a gun. 

Classification. — Primers are classified according to the 
method by which they are fired, into — 
i. Friction ; 
2. Electric ; 
and each of these may be either common or obturating. 

A common primer is one which ignites the charge, and 
is blown out of the vent, allowing the gas of the charge to 
escape through the latter. 

An obturating primer is one which remains seated in the 
vent at discharge, and prevents the escape of gas through 
the vent. 

The primers used with small-arm ammunition will be 
explained later. Those used with cannon are described 

Requisites. — Primers should be safe in handling, not 
liable to damage or accident in store, and certain in action. 

The requisite of safety in handling prevents the use of 
mercuric fulminate, except in the small-arm primers. As a 
general rule mercuric fulminate cannot be used where it is 
exposed to friction of any kind. Hence in fuzes it may be 
safely used, since all the parts are relatively fixed, and well 
protected ; but this is not the case with primers. 

Common Friction Primer. — This primer, (Fig. 199), is 
composed of two copper tubes, a and b, at right angles to 
each other ; a copper wire, c, flattened and roughened at one 
end ; a charge of powder filling the tube a ; and a friction 



composition of antimony sulphide and potassium chlorate, 
filling the tube b. 

The tubes a and b are each made from copper disks, a' 
and b', by the successive action of punches and dies, by 
which the diameter and thickness of the tubes are decreased, 
and their length increased, as shown in the figure. After 
the proper length and diameter of each have been obtained, 
a hole is drilled in the side of the tube a, near its head, the 

Fig. 199. 

tube b soldered to a, the wire c inserted through the hole 
in a, its rough end resting in the tube b, which is then filled 
with the friction composition in a moist state, and the end 
of b closed on the wire, to hold the latter in place. The tube 
a is filled with small-arms powder, and its lower end closed 
with a wad of wax. The outer end of the wire c is formed 
into a loop, for the attachment of the hook of the lanyard. 

ACTION. — When the wire is pulled by the lanyard, the 
roughened edges fire the friction composition in the tube b, 
and this ignites the powder in a. 
191. Common Electric Primer — Action. 

It is often necessary to fire at a distance from the gun, 
as in experiments ; or from a central station where the ob- 



ject can be plainly seen ; or where all the guns of a battery- 
are to be fired simultaneously. 

For this purpose the electric primer is used. 

d V fe ,6 

Fig. 200. 

Common Electric Primer. — The common electric 
primer (Fig. 200), consists of two copper tubes, a and b, 
and two insulated copper wires, c, joined at one end by a 
small platinum wire, /. 

These wires are inserted in a plug of wood, d, and are 
surrounded by a small quantity of dry gun-cotton, e. This 
plug of wood, with its wires and gun-cotton, is inserted into 
the tube a, and the outer end is closed down to hold it in 
place, and the opening filled with wax. The tube b is in- 
serted in a beforehand, and soldered to it, as shown in the 
figure, and is then filled with small-arms powder, and the 
open end closed with wax. 

Action. — When the circuit is closed, the current heats 
the fine platinum wire, /, and this fires the gun-cotton, 
•which fires the powder in the tube b. 

192. Obturating Friction Primer — Action. 

With large guns, the long-continued action of the gases 
under high pressure, erodes the vent rapidly, if allowed to . 
issue freely through it, and hence an obturating primer is 
necessary for these guns. 

Obturating Friction Primer. — The obturating fric- 
tion primer (Fig. 201), consists of a case, a, threaded on the 



•exterior at b, to screw into the vent. A shoulder, c, limits 
the extent to which the case can be inserted. At the rear 
end, d, the case is square, to give a purchase for screwing it 
in and removing it. On the interior, the case is pierced 
with the hole e for the passage of the wire/. This passage 
is enlarged in front and has a cone-shaped surface at g. 
The front of the case is made thin at h, for a reason to be 
given later. The other parts of the primer are a brass wire, 

a "e 

J I *l 

Fig. 201. 

f, roughened at its forward end, and having a conical sleeve, 
i, loose upon it, and a conical enlargement, i'. 

Upon this wire is secured pellet of friction-composition, 
j, and these parts, when inserted into the primer-case, occupy 
the positions shown ; the rear end of the wire being twisted 
into a loop, for the attachment of the hook of the lanyard. 

The front part of the case is filled with small-arms pow- 

ACTION. — The primer is inserted into the vent and 
screwed home, till stopped by the shoulder c. When the 
wire is pulled to the rear by the lanyard, the roughened 
end fires the pellet of friction-composition j, and this fires 
the priming charge. 

The gas may escape in two ways : first along the outside 
of the case and around the screw-thread ; second, through 
the hole e in which the wire rests. 

To prevent escape along the outside, the thin part of the 
■case h, in front, expands under pressure, and fits tightly 
against the walls of the vent, thus forming a perfect gas- 
check. To prevent escape through the hole e, the drawing 
back of the wire/, in firing, brings the conical enlargement 



i' firmly against the front of the sleeve i, and the latter 
against its conical seat, g, in the case, and the gas-pressure 
keeps it in place, thus -closing the hole e. 

193. Obturating Electric Primer — Action. 

Obturating Electric Primer. — This primer is used 
for the same reasons as the common electric primer, and con- 

g* % £ 


Fig. 202. 

sists, (Fig. 202), of a case, a, exactly similar on the exterior to 
that of the obturating friction primer just described. On 
the interior, the forward part of the case b is made thin to 
serve as a gas-check, as before explained. A seat, of the 
shape shown at c, is made near the middle of the case, and a 
hole, d, allows the wires e to pass through. The other parts 
of the primer are, the two insulated wires, e, passing through 
a hard rubber plug, f, and connected at their forward ends 
by a piece of platinum wire, g. A small piece of gun-cotton, 
h, is wound round the platinum wire, and the whole inserted 
in the primer case, occupying the position shown. 

The front of the primer case is filled with small-arms 

Action. — When the circuit is closed, the current heats 
the platinum wire g, and this, fires the gun-cotton h, which 
in turn ignites the powder in the front of the primer case. 

The escape of gas around the outside of the primer is 
prevented by the expansion of the thin portion of the case 
in front, as before. The escape through the hole d is pre- 
vented by the hard rubber plug f, which is forced into its 
seat by the pressure. 



194. Definitions. 

Exterior Ballistics treats of the motion of a projectile in 
air, after it has left the piece. 

The Trajectory, a, Fig. 203, is the curve described by 
the centre of gravity of the projectile during its passage 
through the air. 

Fig. 203. 

The Line of Fire, be, is the prolongation of the axis of the 

The Plane of Fire is the vertical plane containing the line 
of fire. 

The Line of Sight, def is the straight line passing through 
the sights and the point aimed at. 

The Plane of Sight is the vertical plane containing the line 
of sight. 

The Angle of Sight, s, is the angle made by the line o£ 
sight with the horizontal. 



The Angle of Departure, g', is the angle made by the line 
of departure with the horizontal. 

The Angle of Elevation, <t>, is the angle made by the axis 
of the piece with the horizontal. 

The angle of elevation generally differs slightly from the 
angle of departure, owing to the movement of the gun at 
discharge. This movement is due to the elasticity of the 
parts of the carriage, and the lack of accurate fitting of the 
trunnions in their beds, the play of the elevating device, etc. 

The Jump, j, is the difference between the angle of de- 
parture and of elevation, and must be determined by exper- 

The Angle of Fall, go, is the angle made by the tangent to 
the trajectory with the horizontal at the end of the range. 

The Range, bh, is the horizontal distance from the muzzle 
to the point where the projectile strikes. 

Initial Velocity is the velocity of the projectile at the 

Remaining Velocity is the velocity of the projectile at any 
point of the trajectory. 

Final Velocity is the velocity of the projectile at the end 
of the range. 

Drift, kf is the departure of the projectile from the 
plane of fire, due to the resistance of the air, and the rotation 
of the projectile. 

Direct Fire is from guns, with service charges, at all 
angles of elevation not exceeding 15 . 

Indirect or Curved Fire is from guns, with less than service 
•charges, and from howitzers and mortars, at all angles of 
elevation not exceeding 15 . 

High-angle Fire is from guns, howitzers, and mortars at 
all angles of elevation exceeding 15 . 

195. Forces Acting on a Projectile — Circumstances of Motion — 
Forces Acting. — In the case of an oblong projectile, 
which is the only one considered, a motion of rotation about 
its longer axis is given to it, by the rifling of the gun, as it 
passes through the bore. When it leaves the bore, it is sub- 


jected .to the action of gravity, and the resistance of the air. 
It is therefore a free body, having a motion of translation 
and of rotation impressed upon it, and acted on by the two 
forces above mentioned. 

Circumstances of Motion. — The exact motion of the 
projectile under these circumstances is very complex, and 
is discussed in mechanics under the subject of " Rotation." 

The general result of the action of the forces may be 
stated as follows : 

When the projectile first issues from the piece, its longer 
axis is tangent to the trajectory. The resistance of the air 
acts along this tangent, and is at first directly opposed to 
the motion of translation of the projectile, and hence its 
resultant coincides with the longer axis, and it exerts no 
effort to overturn the projectile about its shorter axis. 

The longer axis of the projectile, being a stable axis of 
rotation, tends to remain parallel to itself during the passage 
of the projectile through the air, but the tangent to the 
trajectory changes its inclination, owing to the action of 
gravity. The resistance of the air acting always in the 
direction of the tangent, thus becomes inclined to the longer 
axis of the projectile, and for projectiles in our service, and 
modern projectiles generally, its resultant intersects the 
longer axis, at a point in front of the centre of mass. 

In Fig. 204, G being the centre of mass, and R the re- 

Fig. 204. 

sultant resistance of the air, this resultant acts with a lever- 
arm /, to rotate the projectile about a shorter axis through 
G, perpendicular to the plane of fire. 

If the projectile possesses sufficient energy of rotation 
about its longer axis under these circumstances, the rotation 
about the shorter axis will not occur, but the practical re- 
sult will be, that for projectiles rotating from left to right, as 


in our service, the point of the projectile will move- slowly 
to the right of the plane of fire. As soon as this motion of 
the point to the right occurs, it causes a relative change in 
the direction of the resistance of the air, and an oblique 
pressure is produced on the, left side of the projectile, by 
which it is forced sidewise to the right, out of the plane of 
fire. At the same time, the resultant of this new oblique 
pressure, and of the rotation, causes the point of the pro- 
jectile to move downward. 

The result of the continued action of these forces is 
practically — 

i. To cause the axis of the projectile to describe a cone 
about the tangent to the trajectory. 

2. To force the projectile bodily to the right, and out of 
the plane of fire. 

Drift. — This departure of the projectile from the plane 
of fire, due to the causes above mentioned, is called drift, 
and may be computed by Mayevski's formula, which will 
be given later. The actual motion of the projectile is more 
complex than that above given, and its full investigation 
requires analytical methods. 

196. Form of Trajectory — Causes Affecting Resistance— Form — 
Cross-section — Density of the Air. 

Form of Trajectory. — From the above it appears, that 
the trajectory is not a plane curve, but one of double curva- 
ture. It is also shown by analytical methods, that the drift 
increases more rapidly than the range, and hence the pro- 
jection of the trajectory on the horizontal plane, is convex 
to the horizontal projection of the line of fire, Fig. 203. 

The trajectory ordinarily considered, is the projection of 
the actual curve upon the vertical plane of fire. This pro- 
jection so nearly agrees with the actual curve that the re- 
sults thus obtained are practically correct, and the advan- 
tage of considering it, instead of the actual curve, is, that we 
need consider only that component of the resistance of the 
air which acts directly along the longer axis of the projec- 
tile, and which is directly opposed to the motion of transla* 


Causes Affecting Resistance. — The resistance of the 
air to the motion of a projectile varies with — 
i. Its form ; 

2. Its cross-section ; 

3. The density of the air ; 

4. The velocity of the projectile. 

Form. — Experiment shows that the ogival form of head 
offers less resistance than any other, and the radius of the 
ogive has been increased up to 2 and 3 calibres. Beyond 
this latter radius other considerations, such as strength to 
resist deformation, etc., enter. The resistance depends 
principally upon the form of the head near its junction with 
the cylindrical body of the projectile, as this affects the flow 
of the air over the projectile. The shape of the rear portion 
of the body also affects the resistance, and a projectile which 
is barrel-shaped in rear, such as the Whitworth, offers less 
resistance than one cylindrical in form, for the same reason 
as above. Practical considerations of ease of manufacture, 
facility of packing, etc., have, however, prevented the adop- 
tion of the Whitworth shape. 

Cross-section. — Numerous experiments show that the 
resistance of the air varies directly with the area of cross- 
section of the projectile. 

Density of the Air. — Experiment also shows that the 
resistance varies directly with the density of the air, and as 
this density varies with the temperature and pressure, read- 
ings of the thermometer and barometer must be taken, when 
accurate results are to be obtained. These readings are 
, used to calculate the densities, as will be explained. 

197. Relation between Velocity and Resistance — Experiments. 

Experiments. — The relation between the velocity of a 
projectile, and the resistance opposed to its motion by the 
air, has been the subject of experiment from the earliest 
times to the present day. The most notable experiments 
upon this subject are : 

1. Robins in 1742 made the first experiments by means 
of the ballistic pendulum which he invented. His conclu- 
sions were, that up to 1 100 ft.-secs. the resistance is propor- 


tional to the square of the velocity ; at i ioo ft.-secs. the law 
of the resistance changes ; beyond i ioo ft.-secs. the resist- 
ance is nearly three times as great as if calculated by the 
law of the lower velocities. 

2. Hutton in 1790 improved the ballistic pendulum, and 
made numerous experiments with large projectiles. His 
conclusions were, that the resistance increases more rapidly 
than the square of the velocity for low velocities, and for 
higher velocities that it varies nearly as the square. 

3. General Didion made a series of experiments at Metx 
in 1839 an d 1840 with the ballistic pendulum, and spheri- 
cal projectiles of varying weights. His conclusions were,, 
that the law of resistance is expressed by a formula of the 

general form 

R oc a(v % + bif), 

a and b being constants. This formula held for short ranges,, 
but not for heavy charges and high angles of elevation. 

4. Experiments were therefore made again at Metz in 
1857, and with electro-ballistic' instruments. The conclu- 
sions from these experiments were, that the resistance varies 
as the cube of the velocity. Experiments by Prof. Helie at 
Gavre, in i860 and 1861, gave practically the same result. 

5. The most accurate experiments upon this subject were 
made by the Rev. Francis Bashforth in England, in 1865, and 
again in 1880. The advantage of these experiments is that 
they were made with a very accurate instrument, and with 
comparatively modern projectiles. The conclusions in 
general were, that the resistance varies with some power of 
the velocity, and that this power varies with the velocity, 
being generally as follows : 

For velocities between 900 and 1 100 ft.-secs v' 

" " between 1 100 and 1350 ft.-secs v % 

" " above 1350 ft.-secs 7? 

6. The most recent experiments on the subject, and those 
now adopted for use, were made by Krupp in 1881 with 
modern guns, projectiles, and velocities. General Mayevski 
discussed the results of these experiments, and deduced ex- 
pressions for the resistance as follows : 


198. Method of Determining Resistance. 

The resistance of the air is a force expressed in pounds 
per square inch, and it opposes the motion of the projectile 
in its passage. 

The effect of this force is to retard the projectile. There 
are therefore two quantities to be determined : 

i. The resistance, or pressure of the air, in pounds per 
square inch ; 

2. The retardation, or loss of velocity in feet per second, 
produced by this resistance. 

Method Employed to Determine Resistance. — The 
method generally employed to determine the resistance of 
the air, consists in measuring the velocities z>, and v, of the 
projectile, at two points M 1 and M^ , situated at such a dis- 
tance apart, that the path of the projectile, over this distance,, 
may be regarded as a right line ; and also so that the resist- 
ance may be considered constant over this distance. The 
energy of the projectile at the point M t is imv*, and at 
M, , \mv*. Their difference, \m{y? — v£\ is the loss of 
energy over this distance due to the resistance of the air; 
and supposing this resistance constant, and calling the re- 
sistance p, and the path /, we have 

p/= **»(&,'-»,•) (262) 

This, being the mean resistance, corresponds to the mean 
velocity, or — - — 

By properly selecting the points, and varying the veloc- 
ity so as to include all service velocities, we obtain a series 
of values for the velocity and resistance, from which a curve 
can be constructed, giving the law of resistance for different 

The distance between M^ and M^ must be chosen accord- 
ing to the velocities and projectiles used. Thus for low 
velocities, and large projectiles, the distance between the 
points must be greater, since the loss of velocity over a 
given path is less in this case, than for small projectiles 
moving with high velocities. 


199. Modifications of General Method — Eesults — Resistance. 

Modifications. — When the curve of resistance obtained 
by the above general method is plotted, it is found that 
sudden changes occur in it for different velocities. 

Also the above expression does not take account of vari- 
ation in the form and cross-section of the projectile, or in 
the density of the air. 

To have a general expression into which all these quan- 
tities enter, General Mayevski proceeded as follows : 

Denoting the resistance as before by p, the retarda- 
tion is 

M ~ W P ' 

in which M is the mass of the projectile ; 
W, its weight in pounds ; 
g, the acceleration of gravity, 32.2 ft.-secs. 

This expression was placed equal to z^-/(v), in which A 

is a constant to be determined by experiment, C a factor 
called the " ballistic coefficient," and f(v) some function of 
the velocity. Hence we have 

W p = pW ( 26 3) 

The Ballistic Coefficient C. — The value of this coefficient is 

d, W_ 
6 ca" 

C =s-7J>> ( 26 4) 

in which 

#, is the standard density of the air ; 

8, the density at the time of the experiment ; 

c, the coefficient of reduction ; 

d, the diameter of the projectile in inches ; 
W, its weight in pounds as before. 

Substituting the value of C from (264) in (263), we have 
W p = A TWW < 26 5) 


For a given projectile, all the quantities which enter the 
ballistic coefficient C are known, and they take into account 
the cross-section and weight of the projectile, and the den- 
sity of the air. 

The form of the projectile enters in the coefficient of 
reduction c as follows : For projectiles of a standard form, 
or for those with which the experiments are made, the coef- 
ficient of reduction is taken as unity. For those differing 
from the standard, the retardation will be greater or less, as 
the form is less or more suited to overcome the resistance. 
Hence this coefficient will have values greater than unity 
for projectiles whose resistance is greater than the standard, 
and values less than unity for those whose resistance is less 
than the standard. For the older forms of projectiles in our 
service c = i, for the new form c = 0.9 nearly. 

The values of — for all pressures and temperatures in 

practice are calculated and tabulated for use in Table III 
(Ballistic Tables). 

The only remaining quantities in formula (265) are A and 
f{v), and the object of the experiments is to determine the 
values of A and the exponent of v. 

Results. — As a result of the experiments, the general 
value (265) for the retardation assumes the following forms 
for different velocities : 

For all velocities greater than i33oft.-seconds, 

g A 
■ W 9 = ~C^'' lo S^ =4, 1525284; 

1330 ft.-secs. > v > 1 120 ft.-secs. 

g A 

jpP = -^v 3 ; log A = 7-036435 1 ; 

1 120 ft.-secs. > v > 990 ft.-secs. 

g A 

-^P = -£V*- log A =17.8865079; 

990 ft.-secs. > v > 790 ft.-secs. 



g A ■ 

log A — 8.8754872 ; 
790 ft-secs. > v > 100 ft.-secs. 

A - 

log A = 5.7703827. 

w p =c v ° ; 

Resistance. — The corresponding resistance in pounds 

is obtained for each velocity by multiplying by — since 

W A,. , * cd* A ,, . 


200. Trajectory in Air — Nomenclature — Equations of Motion. 

Nomenclature. — Considering the motion of translation 
only, and that the resistance of the air is directly opposed 
to this motion, let (Fig. 205). 

Fig. 205. 

R be the retardation due to the resistance of the air, its 
value being given by equation (265) ; 

V, the initial velocity ; 

v, the velocity of any point of the trajectory whose co-ordi- 
nates are x and y ; 

z/,, the velocity in the direction of x; 

(/>, the angle made by the tangent to the trajectory with the 
horizontal, at the origin ; or the angle of elevation ; 

6, the value of for any other point of the trajectory ; 

x and y, the co-ordinates of any point of the trajectory, in 

X, the whole range in feet. 

Equations of Motion. — The only forces acting on the 

projectile after it leaves the piece, are the resistance of the 

air and gravity. 


The resistance of the air is directly opposed to the mo- 
tion of the projectile, and continually retards it. Gravity 
is supposed to act vertically, and retards the projectile in 
the ascending portion of the trajectory, while it accelerates 
it in the descending portion. 

Considering the ascending portion, we have for the ac- 
celeration along x, since gravity has no component in that 

dv. „ 

-~ = -R cos 6; (267) 

from this 


dt — = (268) 

R cos 6 v ; 

The velocity along x is 
and along y, 

£\ = -jy- = v cos d ; (269) 


j— = v sin 8 = Vt tan 6 (270) 

Substituting the value of dt from (268) in (269) and (270), 
we have 

v x dv x 

dx= -R^ro> ( 27I > 

v. tan dv, , 

*=" Rcos9 ^ 2 ) 

The acceleration along the radius of curvature is 


-=gcosd (273) 

Substitute in this for r its value — ^ from calculus, 

and we have 

v* ds 1 dsdd dd 

- = v d 7- r =-*d7d7 = - v d;=e cos6 '- < 2 74) 



g cos 6 dt 


Substitute in (275) for cos its value from (267) and for 
v its value from (269), and we have 


g cos 6 dv, 


Collecting these equations, we have 

dt = 

dx = 

dy = — 


R cos & ' 

R cos ' 

v, tan dv, 
R cos 6 


g cos dv, 
' Rv, ' 


If these equations could be integrated directly, they would 
give the values of x, y, t, and for any point of the trajectory. 
But as they are expressed in terms of R, v, , and 6, three in- 
dependent variables, the direct integration is impossible. 

201. Method of Integrating liquations A. — 1st Step. 

1ST Step. — The first step in the process of integration is 
to replace R by its value from equation (263), 


g P = p{v), 


and to make 

f(v) = v" (277) 

in which n represents the exponent of the power of v which 
is proportional to the retardation, for any particular velocity, 
and, according to Mayevski's experiments as shown, varies 
from 2 to 6. 

From equation (269) we have 

v, = v cos 6 ; 





cos" 0' 


Making these substitutions in the value of R above, we 

*=WP = 

A v," 

W ~ C cos " ff 


Substituting this value of R in the first, second, and 
fourth of equations (A), we have 

C dv. 

dt= — -p cos"" 1 6 — • 
A v* 

C ,. dv. 

dx=i — — cos" -1 — — - 

A v " * 


C£"^c-+.fl *!• 


« + 1 * 

A v; 

Dividing both terms of (282) by cos' 6, we have 
dB g C dv. 

cos a 0~ A 

n+ I ' 

or, since cos 8 = j, 


<rC <&\ 

cos a 6 1- A sec"- 1 0v 1 n + I ' 
Collecting these equations, we have 
dti gC dv, 



sec" -1 6* 

Wi - + .- 

dt = 





sec" - 

1 6» 7'," ' 

ak = 




sec" - 

'dv"- 1 ' 









202. Method of Integration of Equations (A) — 2d Step. 

2D Step. — In equations (285), deduced by the 1st step, 
the first members are exact integrals. The second members 
are not, however, because they contain the two independent 
variables sec" -1 and v t . For all cases of direct fire the 
value of sec' 8 differs but little from .unity, since for angles 
of 15°, sec 6 — 1.035, an d for angles less than this, its value is 
still more nearly unity. Hence sec 8 can be replaced by 
unit)- without great error. 

Siacci shows, however, by analysis, that a more correct 
value for direct fire is 


1 = sec" - 2 0, 


and this value has been universally adopted. 

Substituting this value of sec" _ * in equations (285), we 




cos 1 


sec" _ 2 

v * + i> 







— 2 


A sec" - 2 v," - 


Taking the first of equations (287), multiply the numer- 
ator and denominator of the second member by sec" = 
sec" sec 0, and we have 

dO _ g C sec *<(> sec <t>dv t 
cos" B ~ A sec"+ x <pv, n + 1 ' 

But sec "0= — -j^t, and since is constant, sec dv, = 

d (v, sec 0); hence 

dO gCd(v, sec 0) 

cos" ~~ A cos" (v v sec 0)* + l ' 

and by the 
placed Jj 
be i; 

process the other two equations may be 
which the second members can readily 
ce we.Jhaye 

dQ g C d(v 1 sec 0) 

cos* A cos 2 (w, sec cpy + * 

dt=— C d ( v > sec &) . 
A cos (w, sec 0)" ' 

dx ■= — 

•£7 ^d(v t sec 0) 
^4 (z>, sec '</>)" - : 




v cos 

v, sec = -r- = fc, 



K, sec = -7- = V, 



from equation (269), and integrating equations (288) between 
the limits and 6 to which correspond f and «, we have 

tan — tan 6 = — j— — - — -jy- \- . (291) 

nAcos 0L«" P"J v y ' 

b^T-W^J 5 ■ • (292) 


(n — \)A cos 

*-( W _ 2 )^L"- 2 r«-*J ( 


203. Simplification of Equations (291), (292), and (293)— Method 
of Calculating the Functions which Enter them. 
Simplification. — To simplify equations (291), (292), and 
(293), make 



uA V 


+ Q; 

S V> = (n-2)A*- +< *"' 




Making these substitutions, equations (291), (292), and 
(293) can be written, 

tan^-tan^^^j/C*)-/^)}; . (B) 



cos <p , 

> = -- -\.T(u)-T{V)); (C) 

x = c\s( K u)-S(V)\; (D) 

cos d , „ . „. 

u = v ^^' see ^ 2S 9) ( p ) 

In equations (294), (295), etc^ the expression I{u), is 
called the inclination function, T («) the time function, and 
S(u) the space function; Q, Q\ Q" ; , etc., are arbitrary con- 
stants. The values of these functions may be calculated 
and tabulated for convenience, and the resulting tables are 
called " Ballistic Tables." Those used in the present course 
were calculated by Capt. James M. Ingalls, 1st Artillery, 
U. S. Army. By their use the calculation of these functions 
is avoided for any particular case, and the use of the formu- 
las facilitated. 

Calculation of Functions. — As an illustration of the 
method of calculation, take the T(u) function, equation (296): 

In this equation, n is the exponent of the power of v to 
which the resistance of the air is proportional ; A, a constant 
determined by Mayevski's experiments, as explained ; and 
Q" an arbitrary constant. 

For values of v greater than 1 330 f t.-secs., we have n = 2 
and log A = 4.1525284. Hence for these velocities we have 

[4.1525284]* * 
The ballistic tables are so constructed that all the func- 


tions S(u), T(u), etc., reduce to zero for u = 2800 ft.-secs. 
Hence we have 

7» = -= + Q" = o, 

[4.1525284] X 2800 

and solving 

0" = - 2.5137. 

When the velocity is 1330 ft.-secs., n = 3 ; log A = 
7.0364351 ; hence 

} ~ 2 x [7.0364351] x T330 2 

But to avoid abrupt changes in the table, the value of 
T(u) for 1330 ft.-secs. must be placed equal to that which 
would be obtained if n = 2, or from the first equation in 
which Q" enters. This may be done, since Q/' is arbitrary, 
by placing 

-= 2.5137= = - =, + &". 

[4.1525284] X 1330 2 X [7.0364351] x 1330 

Solving with reference to Q", we have 

0," = +0.1791. 

Therefore, for all values of u or v greater than 1330 ft.- 
secs. the value of T(u) is calculated by the equation 

T(u) = — — 2.5137, 

[4.1525284] X« 

and for all values of u or v between 1330 and 1120 ft.-secs. 
by the equation 

T(u) = = -4- 0.1701. 

2 x [7.0364351] X« 2 

Below 1 1 20 ft.-secs. we make a similar change, equating 
the known value for 1120 with the new values for A and n, 
and determine the new arbitrary constant as before, and so 
on for all the functions. 


204. Relation between x andjy. 

We have from equation (B), since tan 6 = -f- 


%- = tan ^— I /(«) - I{V) \, 

dx ^2 cos 4> I v ' v ' ) 


2 -^ ||- tan *}-/(F) = -/(*), • (298) 


v, = z> cos 

. w cos & . 

v. sec = -7- = « (see 289), 

1 cos v *' 

d (z>, sec 0) = du. 

Whence, substituting in the third oi equations (288), we 

C du 


dx du 

-C = -A^ (299) 

Multiplying (299) and (298) together member by member, 
we have *• 

Integrating and making x and y both zero at the origin, 
where u=V, we have 

2 cos 



I ri{u)du 

a w = -~aJ «■-« ' 

we have 
2 cos" j 

|j/-^tan0[--^^=-{^(a)-^(F)}.( 3 oo) 


From equation (D) we have 

£=S(u)-S(V). ..... (301) 

Dividing (300) by (301), member by member, we have 
2cos 2 0(j . , ) rfrr . A{u)-A{V) 

or finally, 

S=-*-i^!4^ ( V?-^}..(E, 

In this equation A (u) is called the altitude function. 
Collecting these equations, we write 

tan* = tan0- 2 -^j/(«)-/(F)(; . . . (B) 

' = ^*{ T M- T W}-' ■ ^ 

x=c\s{u)-S{V)\\ (D) 

X 2 cos 4> I S{u)— S(V) K ' ) K ' 

COS d ,_. 

u = v (F) 

cos <t> 

These are the fundamental equations of Exterior Ballis- 
tics, and the object now is to explain their modifications and 
methods of use. 

205. Modifications of General Formulas for the Whole Range X — 
For the Summit of the Trajectory. 
Modifications for Range X. — The range being the 
distance from the muzzle, to the point where the projectile 
in the descending branch of the trajectory, pierces the hori- 
zontal plane through the muzzle, we have for' this point 

x = X; 
- 6 = 00; 
y = o; 
t= T: 


and making these changes in (B), (C), (D), (E), and (F), we 

tanca = rc^i /( *" )-/(F) }~ tan0; - * (B ° 
X=c{s{u m )-S(V)}; (D') 

-"=H^7$-'<">}' ■ ■ • < E '> 

cos oo ,-p, 


Combining (B') and (E') and eliminating I(V), we have 

C I T . . A(u m )-A{V) } 
tan cj = — — 5-r i /(k m )- c , x _ citss V-- • (*J) 

2 cos J I /( *- )_ 5(«.) - 5(F) } 

Summit of Trajectory. — For this point we have = o, 
and since 

sin 2<p = 2 sin <p cos <p, 

we have from equation (B) 

/(«.) = S -^ + /(H (303) 

and from (F) 

«o = — ^ (304) 

cos 4> v 7 

in which u a and w„ are the values of u and ^ for the summit 
of the trajectory. 

Substituting in (E') for 

its value from (303), we have 


((*.)=c7^ c7r^> . . . . (305) 


and this value in (E') and (G) gives 

sin 20 = c{ /(a.)- I{V) J;. . . . (306) 

tan&5 = 2^oW{ /( ^- /W }- ' (3 ° 7) 

When and co are both small, as in direct fire, we may 
without material error suppose 

</j — 00, 

2 cos " <p tan 00 = 2 cos a ca tan ca = sin 2a> ; 

and substituting in (307), we have 

sin 203= C< /(«„) — /(«„) [ . ... (308) 

206. Auxiliary Formulas. 

Equations (E), (E'), and (G) can be more readily used for 
calculation, if the quantities 

A(u)-A(V) _ 

s (u)-S(V) ^ V) W 


' w s(u)-s(vy w 

are calculated and tabulated for use. 


These quantities are functions of -^ an d f> as ma y be 

shown in the following manner: 

Suppose it is required to compute the height of trajec- 
tory y, by (E), angle <p by (E'), and angle 00 by (G), having 
given the ballistic coefficient C, the initial velocity V, and 
the whole range X, or part of the range x. 

In equation (E), <p and u are unknown. 4> can be com- 
puted from (E') when («„) is known, and 00 in (G) can be 
computed also when («„) is known. 

Hence («„) is the only unknown quantity required to 
complete the solution. «„ can be found from (D'), since 

■£+S{V)=S{u m ) t 


and u can be found from (D) since 

?+S{V) = S(«). 

It follows from this that the quantities (a) and (b) are func, 

X x 

tions of -pr, or -=. and V, and therefore the values of these 

expressions when tabulated should have -= and V as argu- 


We therefore place 

A(uJ)-A(V) r(Jr ._ A . 

A(u„)-A(V) _ 
' {Ua) S{u„)-S(V)~*' 

A(u)-A{V )_ 

S{u)- S(V) KV) *' 

W S(u)-S{V) 

7(u)-I(V) = a + b =m, 




and making the corresponding changes in equation (B), we 

m C 

tan 6 = tan 

In (E), 
in (£'), 

2 cos s <t> ' 

tan 8 = tan ^| 1 : [ . 

( sin 20 ) 

y 4. ^. a C 

- = tan0 


2 COS* 

^ = x tan J 1 ^ — - [ , 

J t sin 20 ) 

sin 20 = ^C, ..... 



in (G), 

tan a> — — (317) 

2 cos <p \o it 

and for small angles of elevation, since 

<P = <», 
we have, from (317), 

sin 2&3 = i? C. (318) 

Substituting in (314) and (315) for sin 20 its value from 
(316), wejiave 

tail 6 = tan <p j 1 - ^- J ; . . . . (319) 
^ ■ = * tan J 1 - J J . . . . (320) 

The auxiliary quantities a, b, A, .£, m, are generally 
written a =f(zV), &=f(sV), m =/(zV), etc. 

207. Explanation of Ballistic Tables. 

The values of the quantities A («), S(u), T(u), etc., have 
been calculated and tabulated as before explained, and their 
values are found in Ballistic Table I, for all velocities from 
2800 to 400 ft.-seeonds, for ogival projectiles. Table II 
gives the value of the corresponding quantities for spherical 

In these tables u is a general expression for velocity, 
so that if v or V be given, its value will be found in the 
column headed u in the tables. 

To illustrate their use, find the values of the different 
functions from Table I, for a velocity of 1 137.6 ft.-secs. 

We have from the table 

S(u) =5(1137.6); 5(1137) =6413.2; 

5(o.6) = 4.26 — 7.1 X .6' = 4.26. 
5(1137.6) = 6408.9 

A (») = A (1 137.6); A (1 137) = 341.73 ; 

A (0.6) = .636 = 1.06 X .6 = .636. 
A (1137.6) = 341.09 


/(«) = 1(1137.6) ; /(i 137) = 0.14942 

I(o.6) = .000216 = 00036 X .6=.ooo2i6 
7(l 137.6) = 0.14920 

7» = 7-(ii37-6); ^(1137) = 3.736 ; 

7^(0.6) = .0036 = .006 X .6 = .0036 
7X1137.6) = 3-732 

Conversely, having the values of the quantities 5 («), 
A(u), etc., to find the corresponding values of u, we proceed 
as follows : 

Find the value of u for 

S(u) =6430.7; 
A (u) = 360.9 ; 
I(u) = 0.1580; 
T ( u ) = 3-720. 
From Table I we have 

S(u)- 6427.4, « = 1135, 
6430.7 - 6427.4 = 3.3. 

Tabular difference for 1 ft.-sec. = 7.2. 

7.2 : 3.3 : : 1 : x 
x = 0.46 ft. -sees., 

u for S(u) = 6430.7 = 1 135 — 0.46 = 1134.54 ft.-secs.; 
A (u) = 360.45, u = 1 1 20 ft.-secs.; 
360.9 — 360.45 = 0.45. 

Tabular difference for 1 ft.-sec. = 1.15. 
1.15:0.45:: 1 :x; 

x = 0.39 ft.-secs.; 

u for A (u) = 360.9 = 1 120 — 0.39 = 1 1 19.61 ft.-secs. 


The same method applies to all other cases, and it is 
evident that the table is used like a table of logarithms. 

208. Auxiliary Tables— Values oi/(zV), z, and V. 

These tables are found in Ballistic Table I, and give the 
values of the quantities A,B,a, b, and m ; and the tables are 
headed " auxiliary A" "auxiliary B," and "auxiliary m." 
The values of a and b are taken from the table for A and B, 
since a and b are general cases of A and B. The expressions 
for these quantities are given by equations (309) to (313), and 
their values were calculated and tabulated by Capt. Ingalls. 

By referring to the tables it will be seen that the argu- 

x X 

ments are z and v. z is used for brevity in place of -~ or -=, 

and hence the value of z is 

x X 

2=2 ~c or ~c ^ 2I ^ 

In this table there are two columns of differences, A z and 

A z corresponds to differences in the argument z, and A, to 
those of the argument V. 

Use of Tables. — We may have the following cases : 

1. A given value of z and one of V, neither of which is 
found in the table ; to find the corresponding value of A, B, 
or m. 

2. A given value of A, B, or m and one of V, neither of 
which is found in the table ; to find the corresponding value 
o f z. 

3. A given value of A, B, or m, and one of z, neither of 
which is fo.und in the table ; to find the corresponding value 
of V. 

Suppose we have a value of z and one of V given, and 
the corresponding value of A, B, or m is required. 
Let / (z V) denote the value sought ; 

z a and V the next smaller values of z and V found in 

the tables ; 
/ (z V ) the value from table corresponding to z„ and 


For an increase of ioo in z, we find that/(^, f ) increases, 
by A, ; hence, for an increase of z — z„ , the increase in 
f(z,V.) will be 

IOO : z — z„ : : A, : x ; 

z — z 

x = A,. 

ioo ' 

Again, for an increase of 50 ft.-secs. in V, f(z, V ) decreases 

by A„ ; hence, following the same rule, the decrease for 


V — V 
x ' — _ 1° 4 

* ~ 50 - - 
The true value oi/(zV) then will be 

A =f(zV) =/{z,K) +^=^ A.- -^^ A v . (322) 

Suppose now we have given f(zV) and V, and wish to 
find z. 

Solving equation (322) for z, we have 

*=*. + ^{^i^^.+/(*n-/(*.^}- (323) 

Or, having f(zV) and £, required F. Solving equation 
(322) for V, we have 

F=F »+£i i ic?^ +/ ^ F;) ~ /( "' F) l-- (324 > 
209. Examples of Use of Auxiliary Tables — Ballistic Coefficient— ~. 

Example i. Find the value of A = /{zV) for z = 1446.7 
and V— 1224.4. 

In formula (322) we have 

z, = 1400 ; 
V n = 1200; 
/(^^.) = -0352; 
A, — .0028 ; 
A v = .0025 ; 
z — z a — 46.7 ; 
V-V a =2 4 .4. 



A = f{zV) = .0352 + ^ x .0028 - ^ X .0025, 

f{zV) = .0352 + .0000876 = .0353. 

In a similar manner B —/(2 V), and m = f(zV) may be 
found by using the proper tables. 

Example 2. Finds for B=f(zV) = 0.1430, and V= 1740. 
In formula (323) we have 

z„ for ^(1700) and B (.1409) = 5100. 

A z = .0046 ; 

4, = -0054 ; 
F- F = 4 o; 
/W = 0.1430; 
S{*M = 0.1409; 

F = 1700. 


. 100 ( 40 ) 

z= 5ioo+-^^|^-x .0054 + 0.1430 -0.1409 J, 

z = 5239.5. 

In a similar manner, having / {z V) = A or m, z may be 
!found, using the proper tables. 

Example 3. Find V for m = f{zV) = 0.2400 and z = 5250. 
In formula (324) we have 

V % for m (.2331) and z, (5200)= 1750, 

4, = .0101 ; 
A, — .0072 ; 
z — 2. = 50 ; 

/K^.) = -233i; 
z, = 5200 ; 
f(zV) = .2400. 

F= 1750 + -^ J ^ X .0072 + .2331 - .2400 J . 
V= ! 733-67- 


In a similar manner, having f{zV) = A or B, V may be 
found, using the proper tables. 

Ballistic Coefficient. — The value of this coefficient 
is given by equation (264), and its calculation involves that 

At rt 

Calculation of -r 1 . — The values of -* 1 are given in Table 

III, for degrees Fahrenheit from o° to ioo°, and for heights 

of barometer from 28 to 31 inches. To find the value of -p 

f or any intermediate values of F and H not in the tables, we 
proceed exactly as in the case of the auxiliary tables. 


Example. — Find the value of -g- for F = 49°.6 and H = 

29.30 inches. From Table III we have 


For F= 49° and H = 29 inches ; -p = 1.012 ; 

Difference ~ f or i° F= + .002 ; 

Difference for o°.6 = + .0012 ; 

Difference ^r for 1 inch H = — .034 ; 

Difference for 0.30 inch = — .0102. 

-^ iorF= 49°.6 and H— 29.30 inches = 1.012 + .0012 — .0102- 

-^= 1.003. 


210. Kind of Fire to which Formulas Apply — Problem I — Use of 
Equation D. 
Kind of Fire. — The formulas above deduced apply 
strictly to direct fire only, where the values of and 6 are 
so small that Siacci's value of sec may be used without 
appreciable error. 



The formulas give, however, sufficiently accurate results 
for indirect or curved fire, and hence they are used for both 
direct and curved fire ; but for mortar fire they must be 
modified, as will be explained. 

Problem I — Use of Equation (D). — Assume equa- 
tion (D), 

Since C is generally known, we have in this equation 
three quantities, x, u, and V, any two of which being given, 
the third can be found. Solving equation (D) for each of 
the three quantities, we can write 

S{u) = £ + S{V); 

S(V) = S(u)-£; 
or, since 

z = 


the two latter can be written 

S{u) = z + S{V), 

For the whole range X we have similar equations, 
changing u into « u and x into X. Collecting these equa- 
tions, we have 

x = C[S(u)-S(V)-};' 

S(u) = z + S(V); 

X=C[S(u u )-S(Vy}; 
S{u a )^z + S(V); 
S{V) = S(u„)-z; 
x _ X 

*~ c~ c 




These equations enable us to solve the following prob- 
lems, which may be grouped under Problem i. 



C,u, V 


C, V,x 


C, x, u 


C, u m V 


c, v,x 


6, X, u a 


In this problem, if the angle of elevation does not exceed 
io°, the values of u and v will be practically the same, but 
for angles greater than 10° the value of v must be calculated 
from that of u by equation (F), 


V = u 

cos 9' 

and tor this purpose the value of 6 must be known. 
Its calculation will be explained later. 

211. Problem 2.— Use of Equations (316) and (321). 
Assuming the above equations, we have 

sin 20 = A C; 

x X 


C ~ c 

i. Having C, <P, and V, find the whole range X. 
From (321) we have 

In this equation X and # are unknown. 
But A =/(zV), and from (316) 

_ sin 2<f> 

Hence in the equation A =f{zV), we have f{z V) and V 
given to find z, which is obtained from equation (323), using 
auxiliary table A. 

This value in equation (321) will give X. 



2. Having C, 0, and X, find the initial velocity V. We 


in which A, z, and Fare unknown. But from (316) 

sin 20 

and from (321) 



Hence we have f(zV) and z given to find V, which is 
obtained from formula (324), using auxiliary table A. 

3. Having C, V, and X, find the angle of elevation 0. 

From (316) we have , 

sin 20 = AC, 

in which A and are unknown. But 

A =/(zV), 
in which 

z ~ ~C~' 

and V is given. Hence we can find A by formula (322), 
using auxiliary table A. This value of A in (316) gives 0. 
We have, therefore, for Problem 2, 



C,0, v 
c, 0, X 
c, v,x 


212. Problem 3— Time of Flight. 

1. Having C, <t>, V, and x, find the time of flight for the 
range x. 

From equation (C) we have 


t = 


in which », the velocity at the point #, and t, the time to 
that point, are unknown. 



But we have, equation (D), 

S(u) = 3 + S(V), 

in which z 


and V are known. Hence u can be deter- 

mined, and this value of u in equation (C) will give t. 
If = or < 10°, u = v ; if > io , 

V—U 77. 


2. Having C, 0, V, and X, find the time of flight for the 
whole range X. 

From equation (C) we have 

T =^rA T ^- T ^-} 


in which u m the remaining velocity at the end of the range, 
and T, the time to that point, are unknown. 
But we have, equation (D'), 

S(u„) = z + S{V), 
in which z=-t* an( ^ fare known. Hence u a can be deter- 
mined, and this value of «„ in equation (C) will give T. 

The same remarks apply to u and Fas in i. 

If = or < 5°, cos = i, practically, and we have 

t=c\T(u)-T(V)} ; 

For Problem 3 we have, then, 



c, 0, V, x 
c, 0, V, X 



213. Problem 4 — Angle of Inclination. 

1. Having C, 0, V, and x, find the value of ff, the inclina- 
tion of the tangent at the point x. 


We have, irom (314), 

tan = tan 0! 1 - -£-£. } 
t sin 20 J ' 

in which and w are unknown. We have 

m =f(zV), 

in which m and 2 are unknown. But from (321) 


Z = -Q, 

from which 2 can be found, and hence tn by formula (322), 
using auxiliary table m. 

This value of m in (314) will give B. The value of thus 
found, when substituted in equation (F), will give v when- 
ever <j> > io c . 

The value of 6 may also be calculated from equation 


twi 1 
I — -3- I, 

in which m is found as above, and 

. sin 20 . , _ N 

A = — -^ — (equation (316)). 

2. Having C, <t>, V, and X, find the value of a>, the angle 
of fall. 

We have from (317) 


tan 00 = 

2 cos* 0' 

in which B and «o are unknown. But we have 

in which B and z are unknown. From (321) 


z- c , 

from which z can be found. We have then z and P 7 given,. 


from which B =f(zV) can be found, using auxiliary table B 
and formula (322), and this value of B in (317) will give 00. 
If <f> = or < 5 , we have, equation (318), 

sin 2go = B C. 

214. Problem 5 — Height of Trajectory — Maximum Height. 

Height of Trajectory. — Having C, <P, V, and x, find 
the height of the trajectory at the range x. 

We have from (320) 

y=xtan<f>\j — -j\, 

in which y, a, and A are unknown. From (316) we have 

sin 20 
A =— c~' 

from which A can be determined. We have also 

in which a and z are unknown. But 


Z = -£, 

from which z can be determined, and we have then z and V 
.given, from which we can find a — f{z V) by the use of aux- 
iliary table A, and formula (322). These values of A and a 
in (320) will givey. Equation (315) may also be used. 

Maximum Height. — Having C, <p, and V, find the 
maximum height of the trajectory. 

This will be at the summit of the trajectory, and for this 
point = o. 

We have from (320) 

y = xt'<m<t> \j --^-J, 

in which y, x, a, and A are unknown. 

For the summit of the trajectory make y = y„ and x = x,. 
To find x a , we have, (321), 

x„ = Cz, 
in which x, and z are unknown. Assume equation (319), 

tan = tan <f»\ 1 — j- \. 


Since 6 = o at the summit, we have 

m = A, 

and from (316) 

sin 2<p , _ 

tn = A = — ^ — , (326) 

from which m can be determined. Then m=f{zV\ in 
which m and V are known and z can be found by auxiliary 
table m and formula (322). This value of z in (321) above 
will give x , the range corresponding to the summit. 
In equation (320), since m = A by (326), we have 

* = *. tan * [1 — £]; 


m = a -f- & 

j,, = *.tan0|_ ^ J, 


y„ = jr. tan d> — . . . 

• (327) 

In this equation y, and b are unknown. But we have 
b =f{zV), in which z and Fare known, and hence b can be 
calculated by auxiliary table B and formula (322). This, 
value in (327) will give y t . 

215. Problem 6 — To Determine the Dangerous Space — Rule of 
Double Position. 
Dangerous Space. — The dangerous space is the hori- 
zontal distance over which an object of a given height will 
be struck. Suppose the height of the object is 6 feet If 
we find first the whole range for a given elevation, initial 
velocity, etc., and then find the range at which the height 
of the trajectory is 6 feet, it is evident that for every point 
beyond this latter range, in the descending branch of the 
trajectory, the height will be less than 6 feet, and the object 
will be struck. The dangerous space, then, is the difference 
between the whole range, and the range corresponding to the 
given height. It is also evident that in general there will 
be two points of the trajectory whose heights are the same 


— one point in the ascending branch, and one in the descend- 
ing branch. The point in the descending branch is alone 

The problem then resolves itself into computing first the 
whole range, and then the range whose ordinate is y, and 
taking their difference. 

Data. — The data are C, <t>, and V. 

Method. — To find the whole range X, use the method 
of Problem 2. 

To find the abscissa of the point whose ordinate is y. 
This problem is apparently the inverse of Problem 5, for 
which equation (320) is used ; but on examining that equa- 
tion it will be found that a is a function of x, and hence we 
have two unknown quantities, and the equation cannot be 
solved. The same is true of all the equations into which y 
and x enter ; there is no direct and simple relation between 
them. Hence the problem must be solved by approxima- 

For this purpose combine equations (D), (E), and (303), 

and we have 

2 cos a d> 
I{ K )S{u)-A(u) = —^y + I{u a )S{V)-A{V). (328) 

In this equation we can compute /(«„) by (303), and hence 
all the quantities which enter the second member are 

Represent this known quantity by k. Then we have 

k = I(u t )S(u) — A (u), 

in which u„ is known, and we have to determine the value 
of u by approximation. 

Rule of " Double Position."— For this purpose we 
make use ot a method called the rule of " double position." 
Suppose we have an unknown quantity u whose value is 
sought. Let u x represent a quantity slightly greater than u, 
and a, a quantity slightly smaller. 

Suppose «, substituted for u in the given equation, and 
the latter solved. A certain value will be obtained which 
will be erroneous. Denote the difference between this 
erroneous value and the true value by e x . Similarly, sub- 


stitute « a for u, and denote the difference between the 
erroneous value and the true value by e a . 

Then the hypothesis upon which the rule of double posi- 
tion is based is, that the errors e t and e a in the results are 
proportional to the errors made in assuming the values of «, 
and u v 

The errors in assuming «, and u, are 


— «,; 

and from the above 

hypothesis we 


and by division 

: e s :: u 

-«i : 

u — u 3 , 

fc i — 

e a : e, :: 

u, — u 

,:« — «,; 

e i — e > : e i - u i — u i '■ u — u i > 
which expresses the rule of " Double Position." 

216. Example. 

The above is best illustrated by a numerical example. 
Suppose k = 1 7666. 1, and 7(u Q ) = 1.55658. 
Then we have 

17666.1 = 1.55658 S(u) — A («). 

u 1 = 430 ft.-secs.; 

S(u) = 21579.4; 
A(u)= 15797-3; 
17666.1 = 1.55658 X 21579.4— 15797.3; 

e, = -(- 126.6. 
Again, suppose 

u, = 420 ft.-secs. ; 

S(u) = 21978.7; 

A (u) — 16861.3 ; 

17666.1 = 1.55658 X 21978.7 — 16861.3; 

e, = -3i5-9; 


€,-e,= 126.6 -j- 315.9 = 442.5 ; 

€ .= — 3I5-9; 
«, — », = — 10; 
« — «, = «— 420. 


442.5 : — 315.9 :: — 10 : « — 42c. 

u = 427.139 ft.-secs. 

This value of u in the equation containing S (u) and A («) 

. e, = + 6,6. 

It is necessary therefore to make a second trial. Assum- 
ing u, = 426.8 ft.-secs., and proceeding as before, we find 

e, = - 8.2 ; 
^.nd forming the same proportion as before, we find 

u = 426.9878 ft.-secs., 
and this value of u will satisfy the original equation. There 
is also another value of u which will satisfy the equation, 
but it will readily be seen that it belongs to the ascending 
branch of the trajectory, and is not used. 

Having the value of u for the point whose ordinate is y 
we find x by equation (D), 

* = CJ 5(«)- 5(F)}, 

and the dangerous space is 

S=*X- x. 
As an approximate value for u in making these supposi- 
tions, the value u a for the end of the range may be calcu- 
lated and used. 

217. Rigidity of Trajectory— Drift. 

Rigidity of Trajectory. — In the previous problems it 
has been assumed that the point of fall of the projectile is 
in the horizontal plane passing through the centre of the 
muzzle, or that the right line drawn from the centre of 
the muzzle to the end of the range, or the chord of the 
trajectory, is horizontal. 


Suppose, however, as is generally the case in practice, 
that the object aimed at is above or below the level of the 
gun, the angle of elevation or depression being a. 

Then it has been proved analytically that the relations 
existing between the elements of the trajectory, and the 
chord which represents the extreme range, are the same 
within certain limits, whether the chord is horizontal or in- 
clined. In other words, the whole trajectory, with its chord, 
may be revolved a certain distance about a horizontal axis 
passing through the centre of the muzzle, without changing 
the relations between the trajectory and its chord. 

This principle is called the " Rigidity of the Trajectory," 
and its practical use is as follows : 

Suppose we fire at an object whose elevation is a. Cal- 
culate the angle of elevation for the given range, as usual, 
and aim directly at the target with the rear sight set at the 
elevation <f>. The act of aiming at the target gives the 
actual elevation (0 -+- a). If a is depression, it is affected 
with a minus sign. This subject is discussed later. 

Drift. — Mayevski's formula for drift is (see Ingalls' 

Ttu A gCV \B{ii )- B(V) „, T „\ X 

: h cos 3 <p I S(u)- S(V) 
in which 

M w}id& fe*>) 

D is the drift in feet ; 

u = 0.53 for cored shot ; 

u = 0.64 for shell ; 

n = the twist of the rifling in calibres, at the muzzle 

- = 0.41 for projectiles 2.5 calibres long ; 

- = 0.37 for projectiles 2.8 calibres long ; 

- = 0.32 for projectiles 3.4 calibres long ; 

n— 3.1416; 

g = 32.2 feet ; 

C, <P, and Fas in other ballistic problems ; 


B(u), B{V), M(V) are drift functions whose values are 
found from Table I, like those of S{u), A («), etc.; 
X, the range in feet. 

The drift will be more or less affected by the wind, ac- 
cording to its direction and velocity, and its effects will be 
further explained under the subject of Pointing. 

218. Problem 7 — Mortar Fire — Modified Equations — Calculation. 

Modified Equations. — The formulas for direct fire 
were obtained from the differential equations (A) by assum- 
ing that the inclination 6, of the tangent, at every point of 
the trajectory, is relatively small, and hence its cosine or 
secant constant, and approximately unity. For high angle 
or mortar fire, however, such an assumption is manifestly 
incorrect, since the angle 6 varies greatly throughout the 

For mortar fire, therefore, Siacci assumes that there 
is a mean value of C0o 0, which will satisfy the differential 
equations, and make their second members exact inte- 
grals. This mean value is denoted by a, and its value is 

shown analytically to be a = - — ±-J- \_ ' (0) representing 

— , and 8, I —-,, and their numerical values 

cos*^ 1 4> J cos*+ 1 b 

being given in Table IV, together with the values of tan 
<p and tan 6. 

This is applied as follows : In the integration of equa- 
tions (A) in the case of direct fire, the second step consisted 
(see page 360) in substituting for sec" -1 6, the constant value 
sec"" 2 (p. But for mortar fire, ,« must be substituted for 
sec" -1 0, wherever the latter occurs, instead of sec" -2 <p. 

To show the effect of this substitution, take the second 

of equations (285), dt = -. t-.. —. Writing- for sec 

A sec" -1 v„ ° 

its mean value a, we have dt = — - 1 . MultiolvinST 

Act"- 1 v," F; b 

numerator and denominator by a, dt = vf^jj Renre- 

A (av,)" r 


senting av x by u, we have u = av l = av cos 0. Making the 
same substitutions in the remaining equations (285), and 
integrating, we have the following formulas for mortar fire : 

S=C JS(«) -£(£/) j; .... (330) 
t=c{T{u)-T(U)\: .... (331) 
x=~\s[u)-S{U)}; .... (332) 

f=-*-f {4g£$? "'(*>}. • (333. 

in which 5" is the length of any arc of the trajectory, meas- 
ured from the origin ; £/= Va cos <p ; u = av cos ; t' = 
velocity at the point S; 6 = the inclination of the tangent 
at the same point. 

The values of the functions A(u), S(u), etc., can be taken 
from Table I, u and U being first calculated as explained in 
the nomenclature. 

Calculation. — The most important problems in mortar 
fire are to find the whole range X, and the time of flight, T, 
for that range. For this purpose the given data are gen- 
erally C, <p, and V. It is evident, however, that with the 
given data, equations (331) and (332) cannot be solved, and 
the solution is obtained as follows : 

For the end of the range y = o, and from equation (333) 

we have 

2_tan_0 __ A(u m )-A(U ) 

—-£-+I(U)- S{Uu) _ S{U y ■ • (334) 

For mortar fire the angle of fall is very nearly equal to the 
angle of elevation, and under this supposition we have, 
since — 6 = a>, 

(0)-(g) = (0) + Q») ;= _(0) 

tan <p — tan ff tan <p + tan 00 tan 0' 

from which a is known. The first member of equation (334) 
is therefore known, and also A{U) and S(U) in the second 
member. u u is therefore found by " Double Position," as 
previously explained. This value of u u in (330), (331), and 
(332) will give the remaining values sought. 






C,u, V 


C, V,x 


C, x, u 


C, u m V 


C, V,X 

u a 

C, X, u a 


C,cp, V 



C, <p, X 



c, v,x 



C, <p, V, x 






C, <p, V, x 



C,0, v,x 



C, cp, V, x 



c, 0, V 



C,<P, V 



C,<p, v 

Dangerous space 


C,<P, V 



c,<t>, V 



c,<p, v 



c,<t>, v 



C,cp, V 



C,cp, V 



Note. — Ingalls' Ballistic Tables are to be used in these problems, and the 
methods of Capt. Ingalls have been followed in deducing the equations. 



219. Classification — Principal Parts of Field and Siege Gun Car- 
riages — The Axle. 

Classification. — Artillery carriages may be classified 
according to the service for which they are intended, into 
field, siege, and sea-coast carriages. 

Field and siege carriages are generally wheeled, and are 
intended to support the guns in firing, and to transport them 
from place to place, with their ammunition and necessary 
supplies. • 

Sea-coast carriages are intended only to support the 
guns in firing, and hence their construction differs materi- 
ally from that of field and siege carriages. 

Principal Parts of Field and Siege Gun Car- 
riages. — In the field and siege services, the carriage which 
supports the piece, and from which it is fired, is called the 

Its principal parts are : 
i. The axle ; 

2. The wheels ; 

3. The stock or flasks ; 

4. The brakes ; 

5. The elevating device. 

The Axle. — The principal parts are the body, the rein- 
force, and the arms. 

The body is the middle part of the axle, between the 
arms, upon which the heads of the cheeks rest, and which 
bears the weight of the piece and the force of recoil. It is 



generally made of steel, and is solid, as this construction is 
necessary to resist the force of recoil in these carriages. 
Its length is governed by the requirement that the track of 
the wheels shall be the same as that of ordinary vehicles, so 
that it can be used on the same roads. 

Reinforce. — To increase the strength of the axle and 
its resistance to bending under the force of recoil, and also 
to furnish a support for the cheeks of the carriage, the axle 
is generally reinforced. In the old carriages the axle-body 
was enclosed in wood ; in the new field-carriages it is en- 
closed between two steel plates riveted together and fitting 
the exterior of the body accurately. For larger carriages, 
or for those in which the recoil is taken up by hydraulic 
buffers, this is not necessary. 

The Axle-arms. — These form the supports for the 
wheels, and are the axes about which they revolve. The 
arms are made solid, terminating the axle-body. They 
are conical in shape, as this gives stiffness with small 
weight, enables the wheel to be put on easily, insures a 
good fit between wheel and axle-arm, and enables any wear 
to be taken up by means of washers. 

The axis of each arm is inclined slightly downward so as 
to make the lower element nearly horizontal. This causes 
the lower spoke of the wheel to stand vertical, and relieves 
it from cross-strain, and also prevents a thrust upon the 
linchpin. The axis of the arm is also inclined slightly to 
the front, so that when the wheel meets any obstacle in that 
direction it will be free from cross-strain. These two in- 
clinations of the axle-arm are called the " set." The wheel 
is secured on the arm by a linchpin which passes in a 
vertical direction through a hole in the end of the arm, and 
is held in place by a semicircular catch passing under the 

A shoulder on the inside, next the body, holds the wheel 
in place. 

220. The Wheels— Parts. 

The principal parts are, Fig. 203, the central part or 



nave N, the spokes S, the rim R, and the tire T. The nave 
receives the pressure of the axle arm and transmits it to the 
spokes. Formerly naves were made of wood, and lined 







Fig. 203. 

with a metal box, called the nave-box, which diminished the 
wear. Now they are made of malleable cast iron or bronze, 
in two parts, one (a) forming the nave-box and the other 
{b) forming a support for the spokes in front, which are 
inserted between these parts, pressed into place by a strong 
radial pressure, and bolted as shown at d, so as not to 
weaken them. 

By this arrangement a spoke can be readily removed 
and replaced. This construction is used in the Archibald 
wheel, which is adopted in the U. S. service. 

An enlargement c is sometimes made in the middle of 
the nave-box to contain the lubricant. 

The spokes s, receive the pressure from the nave and 
transmit it to the rim. In our service they are made of 
hickory, as this gives great stiffness and elasticity for a 
given weight. 

The stiffness is required to resist the thrust in firing, and 
strength is also required to enable the wheel to be used on 
rough ground, where the spokes are liable to be broken by 
contact with obstacles. The spokes are set at a slight angle 
with the axis of the nave, thus forming a conical surface. 
This is called the dish, and its object is as follows : 

When the ground is inclined, the weight of gun and car- 


riage produces a thrust on the lower wheel in the direction 
of the arrow. If the spokes were per- 
pendicular to the axis of the nave, this 
thrust would cause a cross-strain on 
them, and its effect would be to loosen 
them in the nave, or cause them to 
Fig. 204. work. The dish enables the spokes to 

resist this lateral thrust, and it is converted into a strain of 
compression. The whole structure thus acts as a circular 
truss, the rim being the tie. 

The Rim. — This distributes the weight which it receives 
from the spokes, to the ground. It is generally made of 
wood for the same reasons as in case of the spokes, and in sev- 
eral segments, called felloes. The object of this is to avoid 
cutting across the grain of the wood, and consequent weak- 

The Tire. — The segments of the rim and the spokes are 
held in place by the steel tire T, Fig. 203, which is shrunk 
on, and binds all the parts together. It also protects the 
rim from wear, and when any of the parts become loose, it 
can be removed, shortened, rewelded, and reset. For this 
purpose it is made of low steel. It is held in place on the 
rim by countersunk bolts passing through both. 

221. Object of Wheel— The Stock. 

Object of Wheel.— The object of the wheel is to trans- 
fer the resistance to motion from the ground, where it is 
great and irregular, to the surface of the axle arm, which 
is lubricated, and the resistance of which is consequently 
small and regular. 

The power being applied with a lever-arm, whose length 
is the radius of the wheel, while that of the resistance or 
friction is the radius of the axle-arm, the advantage of the 
wheel as a mechanical power increases with the radius of 
the wheel, and decreases with that of the axle-arm. On this 
account the radius of the wheel should be as great as pos- 
sible and that of the axle as small as possible. 

The radius of the axle-arm is fixed by the requirement 
oi strength to support the shock of recoil; and that of the 


wheel by considerations of weight, draught, and facility of 
turning. A high wheel also is unstable. These considera- 
tions have fixed the diameters of wheels in the field and 
siege services as follows: field service, 57f- inches; siege ser- 
vice, 60 inches. The siege wheel is much stronger and 
heavier than that for the field service. 

An increase in width of rim also distributes the weight 
over a greater area and enables the wheel to better over- 
come the resistance offered by soft ground to traction ; but 
it increases the weight of the wheel and decreases the 
facility of turning. 

The Stock. — This consists of two pieces, called the 
flasks, which are separated at the upper ends, forming the 
cheeks, and which gradually converge at the lower ends, 
and are united there by a solid piece called the trail-plate 
or lunette. The cheeks rest upon the axle body or rein- 
forcing plates, and have on their upper surfaces two trun- 
nion-beds, in which the trunnions of the gun rest. The 
trunnions are held in place by two caps, called cap squares, 
which fit over bolts projecting from the cheeks at the 
extremities of the trunnion-beds, and are fastened by keys 
or bolts. The flasks are also united by various transoms, to 
give stiffness to the structure. The supports for the elevat- 
ing screw or other device are generally attached to the 

The distance between the flasks varies with the size of 
the gun, and should be sufficient to allow the breech to be 
depressed to the maximum extent required in service. By 
this separation, also, the strain due to recoil is distrib- 
uted over a greater length of axle body, and thus the 
resistance to bending is increased. The stock is subjected 
to a strong transverse stress in firing, and hence must be 
designed to resist this. It also acts to couple the gun-car- 
riage to the limber when the gun is to be transported, and 
it gives the necessary third point of support in firing, and 
enables the piece to* be pointed. To it are attached the 
supports for the sponges and rammers, and in general, if 
possible, no parts are allowed to project below the 
plane of its lower edges, to avoid striking obstacles. When 


not required to resist the shock of firing, its use is simply 
to connect the carriage and limber, and its construction 
then differs materially from that described, being much 
simpler and lighter. 

222. The Brakes — Friction-brakes — Shoe — Hotchkiss — Lemoine — 

Brakes. — The object of a brake in the field and siege 
service is to limit the recoil, so that the piece may be kept 
approximately in its firing position, and thus avoid the 
fatigue to the cannoneers of running the piece back over a 
considerable distance to that position after discharge, and 
the consequent delay in loading. 

The principles of brakes will be explained under the 
subject of recoil. 

For the field and siege services they may be divided 
into — 

i. Friction-brakes. 

2. Elastic brakes. 

3. Hydraulic brakes. 

Friction-brakes. — These, as will be seen later, do not 
give the best results, but are sometimes preferred on 
account of their simplicity, and as being less liable to get 
out of order. 

Shoe. — The simplest friction-brake is the shoe, which 
consists (Fig. 205) of a strong piece of iron, a, fitting the 

Fig. 205. 

wheel, and attached by a chain, b, to the stock. It is 
often used in travelling, and transforms the rolling into 
sliding friction. 



The Hotchkiss Brake (Fig. 206) consists of a conical 
box, a, working in screw-threads on the axle-body b. The 
nave of the wheel is also made conical at c. 

Fig. 206. 

By turning the handle d attached to the brake, it is 
screwed up till the conical surfaces are in close contact. 
The friction between these surfaces, when the wheel rotates, 
tends to tighten the brake, and thus increase the resistance to 
rotation, while if the moment of rotation becomes too great, 
the surfaces will slip, and thus prevent destruction of the 

The Lemoine Brake is used in the French service. It 
consists (Fig. 207) of a rope, a, attached to the brake-beam 
at b, and wound loosely around the nave of the wheel. 

This rope is tapering, being larger at b, and gradually 
decreasing in size. It is attached in front to a cross-bar, c, 
and this is connected to the rod d, which moves freely in 
the direction of its length, and carries a heavy mass, e. The 
action of the brake is as follows : When the piece is fired, 
the carriage recoils in the direction of the arrow, while the 
rod d, on account of the mass e, moves relatively forward. 
It is held in this position by the notches on d bearing against 
the edges of the plate through which it slides. This tight- 
ens the cord around the nave of the wheel, and causes it to 
be wound up as the wheel turns. Owing to the increase 

39 6 


in diameter of the rope, it is wound more rapidly as the 
length of recoil increases and its velocity decreases, so that 

Fig. 207. 

the brake is applied gradually. It may also be applied 
by hand, in travelling, by pulling out the rod d by the 
handle d'. 

Nordenfelt Brake. — This is found on the carriage of 
the Nordenfelt rapid-fire gun, and 
also on the Hotchkiss carriage. It 
consists of a frame, one side of which 
is shown in Fig. 208, attached to the 
axle above its centre at the points 
aa ; bb are the brakes, c the rod con- 
necting them, dd rubber washers 
through which the brake-rods ee pass. 
As the points of support a are eccen- 
tric with reference to the axle, when 
the brakes are lowered, they come 
in contact with the wheels, and any 
rotation in recoil binds them still 
more tightly. When not in use, 
they are hooked up to the cheeks of 
the carriage. This brake is elastic 



223. Elastic Brakes— Buffington — Englehardt — Belleville Springs. 

Elastic Brakes. — These check and moderate recoil by 
transmitting the first shock to some elastic body, which 
is thereby deformed, and when this body resumes its 
original form, due to its elasticity, the shock is gradually 
transmitted to the parts of the carriage. This relieves the 
carriage from the sudden shock, and thereby enables it 
better to sustain recoil. 

The Buffington Brake. — This was designed by Colo- 
nel Burlington of the Ordnance Department, and is used 
with the field carriages.' 


Fig. 209. Fig. 210. 

The older form consists of a rod, a, Fig. 209, surrounded 
by a spiral spring in a casing. The outer end of this rod is 
formed into a hook, which fits over the tire of the wheel. 
The casing which carried the rod and spring is attached to 
a hook, b, above the centre of the axle. When the rod and 
casing are lowered, the hook rests against the tire, being 
eccentric to the wheel. Any rotation of the wheel in the 
direction of recoil draws the rod out of the casing, and com- 
presses the spiral spring. The brake is thus gradually ap- 
plied. Various defects in this brake have caused the adop- 
tion of the later form shown in Fig. 210. 

Later form shown in Fig. 210. Instead of the casing 
and spiral spring, the rod is attached to a bow-spring, c, 
which is elongated when the wheel recoils. It is held ver- 
tically when not in use. 

The Englehardt Buffer. — This is used on some of the 
English carriages. It censists (Fig. 211) of an elastic buffer, 

a, of cork, rubber, or springs, which rests against a transom, 

b, attached to the cheeks of the carriage. 

These cheeks have a bracket, c, in front, in which the 
axle d rests, and which allows them to move backward 



independently of the axle, and they are notched in rear at 
e, to allow a motion independent of the cross-bar f. The 
axle is attached to the cross-bar / by the brace g, and this 
attachment is made as near the axle-arm as possible, to 

Fig. 2ii. 

avoid bending. A bolt, h, passes through the buffer a, and 
through a hole in the transom b, and is attached rigidly to 
the cross-bar/. The action is as follows: When the piece 
is fired, the cheeks and transom b recoil together, the axle 
and cross bar sliding in their notches c and e. This motion 
compresses the buffer a, and as it recovers its shape, the 
force of recoil is gradually transferred to the wheels and 
axle, through the cross-bar /and brace g. 

Belleville Springs. — • These are saucer-shaped disks 
of steel, s, Fig. 212, fitted edge, to edge, and kept in place 

Fig. 212. 

by an axial rod, r, for which purpose a hole is pierced in the 
centre of each disk. Since they occupy a relatively small 
space, a large number of them may be employed, and the 
compression of each is small. They are, however, expen- 
sive, and spiral springs are often used in place of them. 



224. Hydraulic Brakes— Elevating Devices — The Elevating Screw. 
Hydraulic Brakes. — These are not used in the field 
service, owing to their weight, and liability to get out of 
order when subjected to rough usage, but they are used in 
the siege carriages, and in general wherever the recoil is 
great, and it is necessary to regulate it very exactly. They 
will be considered under Sea-coast Carriages, where they 
are always used. 

Elevating Devices. — These are used to give the proper 
elevation to the piece, and may consist of — 
A screw ; 
A toothed sector ; 
A combination of levers. 
The Elevating Screw is generally double, and consists 
(Fig. 213) of an exterior hollow screw, 
a, working in a fixed nut, b. 

The exterior of the screw a has a 
left-hand thread, its interior a right-hand 
one. A second screw, c, works in the 
interior thread of a. d is a hand-wheel, 
which is free to rotate, but is fixed to 
the nut b, so that it has no motion of 
translation. A longitudinal channel or 
spline, e, is cut on the exterior of a, and 
a key on d fits this. The action is as 
follows : When d is turned it causes a to 
turn with it, on account of the spline 
and key, and at the same time a working 
in the fixed nut b moves parallel to its 
Fig. 213. own axis. The head of c being fixed 

by a strap, s, to be described, cannot turn, and c is forced 
to move parallel to its own axis by the rotation of a, and 
the action of its interior screw-thread. The resultant 
motion is, for each turn of d, equal to the sum of the pitches 
of the two screws. 

The advantage gained is that we are enabled to use an 
elevating screw, which is short ordinarily, but which can be 
lengthened to give any elevation or depression desired. 
Strap. — To cause the blow on the head of the elevating 




screw, upon firing, to be normal to its axis, and thus avoid 
bending, the nut b, in which the screw works, is arranged 
on trunnions between the cheeks of the carriage, and a 
strap, s, Fig. 214, is attached at one end to the head of the 

Fig. 214. 

screw c, and at the other to an axis, /, parallel and near 
to the axis of the trunnions of the gun. In this way the 
axis of the screw, c, is kept nearly normal to the axis of the 
gun for all elevations. 

225. Elevating Devices— The Toothed Sector — The levers. 

The Toothed Sector. — This is used generally in 
combination with gearing, on the larger guns, it consists 
(Fig. 215) of a toothed arc, a, bolted to the gun, and acted 


Fig. 215. 

Fig. 216. 

on by a gear, b. This gear may be worked directly by a 
hand-wheel, or more frequently by intermediate gearing. 
To gain power, and secure small motions, a worm-gear is 
frequently used. 


The Levers. — A combination of levers, called a 
" lazy-tongs," is used as an elevating device on the light 
3.20 carriage. It consists (Fig. 216) of the arms a, 
jointed as shown and attached at b by a fixed axis to 
the carriage. Two side levers, c, are attached to a fixed 
axis at d on the carriage, and to the arms a at e. A 
screw, f, passes through the other extremity of the side 
levers c, and works in two collars, hh, attached to the car- 
riage. When the screw / is rotated by the handle g, the 
side levers c are raised or lowered, and acting on the arms a 
through its connection e, it causes the structure to elongate 
or contract, and thus to elevate or depress the gun. The 
device is connected with the breech of the gun by a leather 
strap, k, passing over the breech. 

226. Draught — Modes of Work of Horse — Pack-horse — Draught- 
horse — Angle of Traces. 

Draught. — Field and siege carriages are intended not 
only to support their pieces during firing, but also to trans- 
sport them from place to place. For this purpose the 
two-wheeled gun-carriage must be converted into a four- 
wheeled one, by the attachment of a limber. This leads 
to a consideration of the load which can be carried by the 
horse, and the best method of attaching him to the carriage. 

Modes OF Work of Horse. — A horse may carry his 
load on his back, in which case he acts as a pack animal ; or 
he may draw this load by being attached to a carriage, as a 
draught animal; or these two methods may be combined. 

Pack-horse. — This method is only used in the moun- 
tain service, when the roads are impassable for wheeled 
vehicles. Under such circumstances the load for a horse is 
from 200 to 250 lbs., and, if moving at a walk, he can carry 
this load 25 miles in a day. If at a trot, the load or the dis- 
tance, or both, must be reduced. In this case he can carry 
the same load about 17 miles in a day. 

The daily work of a pack-horse is considered equal to 
that of five men. The mule is a better pack animal than 
the horse, as he can carry more, is more sure-footed, and 
eats less. He is therefore generally used for this purpose. 


Draught-horse. — A horse can, by the aid of the wheel, 
draw much more than he can carry, and hence it is always 
advantageous to use him as a draught animal. 

In considering the draught of a horse, his effort may be 
divided into two parts : first, that necessary to start the 
carriage, and second, that necessary to keep it in motion. 

The first being only temporary, may approximate the 
maximum strength of the horse, but it is important to know 
it, as upon it is based the strength of the harness. 

Experiment shows that this effort varies with different 
horses from 600 to 1000 lbs., as measured with a spring 

The second part ot the effort varies with circumstances, 
such as the load, nature of the roads, etc., from ^ to -^ of 
the load. When horses are used together in a team they 
will do less work than the same number singly, owing to 
their interference with each other. 

Angle of Traces. — The angle made by the traces with 
the ground also influences the amount of work done by a 

If the traces be attached to the carriage at a point higher 
than that at which they are attached to his is evi- 
dent that a component of the pull acts upward and decreases 
the hold of the horse on the ground, and, consequently, his 
power to pull. On the other hand, if this point is below the 
point of attachment at the shoulder, the vertical component 
acts in the opposite direction, and increases his hold on the 
ground. Experiment has shown that when the horse car- 
ries no load, the best result is obtained when the traces 
make an angle of from 10° to 12 with the ground. The 
tangent of 12 being about \, this shows that the horse pulls 
best when \ of his load is transferred to his shoulders. On 
the other hand, if a horse carry a load of 150 to 200 lbs., and 
pull at the same time, experiment shows that this angle 
should be 6° or 7 . 

Making allowance for bad roads and rough usage, ar- 
tillery horses draw less than those of commerce, and the 
loads allowed per horse are about as follows : 


Horse artillery, 650 lbs.; 
Field artillery, 700 to 850 lbs. ; 
Siege artillery, 1000 lbs. 

227. Modes of Attachment of Horses — Attachment of Traces. 

Modes of Attachment. — Horses may be attached to a 
carriage in three ways : 

1. In single file, with the wheel-horse in shafts; 

2. In double file, with one of the wheel-horses in shafts ; 

3. In double file, with the two wheel-horses on oppo- 
site sides of a pole. 

The team is ordinarily composed of six horses, arranged 
in pairs. The horses nearest the carriage are called the 
wheel-horses, those next in front the swing-horses, or swing- 
team, and those in front the lead-horses or leaders. 

In each team the left horse is the near, and the right 
liorse the off horse. The near horse carries the driver. 

Single File. — The objections to this method of attach- 
ment are that much of the tractile force is lost, owing to the 
■curving and turning of ordinary roads ; it is difficult to 
make all the horses pull together ; and the shaft-horse, being 
subjected to the irregular action of the other horses of the 
team, is soon worn out. For heavy loads over good straight 
roads at a slow pace, it has the advantage of a direct pull. 

Double File, Wheel-horse in Shafts. — This method obviates 
the defects of the long line of traction on ordinary roads, 
and it controls the movements of the carriage well ; but it 
subjects the shaft-horse to excessive fatigue, and hence is 
not generally used. 

Double File, with Pole. — This method is generally adopted, 
as it gives the advantages of a short line of traction, with 
comparatively little fatigue to the wheel-horses, the con- 
trol of the carriage being effected by two horses instead 
of one. 

Attachment of Traces. — The traces may be attached 
to the carriage by a single fixed bar, a, called the splinter- 
bar, as in the old carriages, or by a double tree, b, which is 
pivoted at its middle point to the pole, and the traces 



attached to each end by a movable single tree, c. Fig. 217- 
shows the old and the new methods. 



Fig. 217. 

The advantage of the old method is that it is simple and 
strong. The disadvantages are that it throws an unequal 
amount of work upon the two horses, so that a willing 
horse will do most of the work, and there is no method by 
which the driver can detect this. Consequently, the re- 
sultant of the traction in this case will not coincide with the 
pole or middle of the axle. 

The advantage of the new method is that it obviates the 
above difficulty, and forces an unwilling horse to do his 
share of the work. The single trees also prevent chafing, 
by yielding to the motion of the horse as he advances his 
shoulders in pulling. 

228. Support of Pole — Line of Draught of Traces. 

Support .of Pole. — The weight of the pole may be 
supported — 

1. By counterbalancing it in rear of the axle ; 

2. By suspending it from the necks of the horses ; 

3. By a combination of these methods. 
Counterbalancing Weight of Pole. — The advantage of this 

method is, that it frees the necks of the horses from the 
weight of the pole, and they are consequently not fatigued 
by it. 

The disadvantages are, that if it is done by placing the 
trunnions of the gun well to the rear on the gun-carriage, it 


causes difficulty in limbering, because of the extra weight 
lifted. If it is done by allowing the trail to project over 
the pintle hook and rest upon a circular sweep-bar, a, Fig. 
218, it is difficult to limber, as the trail must be raised suffi- 





Fig. 218. 

■ciently to pass over the pintle b. As quickness of limbering 
is of importance with field artillery, this method is not used. 

In the siege service, where quickness is not required, 
and where the weights are relatively great, it is used, espec- 
ially the method shown in Fig. 218. 

Suspending Weight from Necks of Horses. — The advantage 
of this method is that the attachment of the trail to 
the limber can be made at the most convenient place for 
limbering, and the weight oi the gun can be thrown so 
far forward as to render the operation of limbering very 
easy. The great objection, however, is that it fatigues the 
horses too greatly, and cannot be used. 

Hence a combination of these two methods has been 
adopted in the field service. To diminish the weight rest- 
ing on the necks of the horses, the ammunition-chest of the 
limber has been placed, so that its centre of gravity when 
loaded is directly over the axis of the axle, and the weight 
upon the trail when the gun is limbered is regulated to 
partly counterbalance that of the pole. 

Line of Draught of Traces. — This is so arranged 
that the line of traction shall be continuous from the lead- 


horses to the carriage, and is accomplished by attaching the- 
traces of the swing-team directly to those of the wheelers,, 
and those of the lead-team directly to the traces of the 
swing-team. By this means each horse pulls independently 
of all the others, and there is no interference. 

229. Turning Angle — Direction of Carriage — Backing. 

Turning Angle. — The angle required to turn the car- 
riage in, is called the turning angle, and is measured by one 
half the horizontal angle through which the pole sweeps. 
In practice an angle of 6o° is sufficient. It varies with the 
arrangement of the horses, the height of the front wheels, 
the length of stock, _the position of the pintle, and the thick- 
ness of the stock at the point where the front wheels strike 
it. Other considerations determine that the height of the 
front wheels shall be the same as those of the rear ones for 
interchangeability, that the length of stock shall be gov- 
erned by considerations relating to recoil, and that the 
position of the pintle shall be considered with reference to 
ease of limbering and weight of pole on the horses' necks,, 
as before explained. For carriages that do not withstand 
the shock of recoil, the length of stock is adjusted with 
reference to the turning angle. 

Direction of Carriage. — This is given by means of 
the pole. The latter being attached to the necks of the 
wheel-horses, the direction may readily be changed by 
directing the wheel-team to the right or left. 

Backing. — The pole is also used to stop and back the- 
carriage. The wheel-horses are attached to the front of the 
pole, as will be explained when the harness is described. 

In stopping or backing the backward thrust of the horses 
is applied at the end of the pole, and this thrust transmitted 
to the rear along the pole to the carriage. 

230. The Harness. 

The harness at present in use for the field artillery was- 
designed by Major Williston of the artillery. That for the 
wheel-team differs slightly from the swing and lead harness.. 
For the wheel-team it consists of — 



1. The head gear to guide- and hold the horses; 

2. The saddle to transport the driver ; 

3. The draught harness, by which the carriage is moved 
forward ; 

4. The breeching, by which the carriage is stopped, or 
moved to the rear ; 

5. The breast straps, by which direction is given to the 
carriage, and the weight of the pole supported. 

For the swing and lead teams the breeching and breast 
'straps are omitted, and the traces are supported by a single 
hip strap. 

Fig. 219. 

Head Gear. — The head gear consists (Fig. 219) of the 
bridle a, by which the horse is guided, and the halter for 
holding him when not in the carriage. 

The bridle and halter are the same as those used in the 
cavalry service. The bridle rein of the off horse passes 
through a pulley on the front of his saddle, so that there is 
a direct instead of an oblique pull, in stopping and backing. 

Saddle. — The saddle x is the same as that used in the 
cavalry service. Each horse is saddled, the saddle being 
held in place and motion to the front prevented by the 
back strap t and crupper t', while the collar is secured to 


the saddle in front by the strap v. The girth strap or 
cincha w prevents motion of the saddle around the horse. 
The near horse carries the driver, and the off horse may 
carry an extra cannoneer. Saddle-bags, b, are used, as in 
the cavalry service, to carry the clothing, etc., of the drivers. 

Draught Harness. — This consists of a collar, c, made 
of U-shaped steel. It is hinged at the top, and closes at the 
bottom with a spring catch. It rests against the shoulders 
of the horse, and is intended to distribute the force of trac- 
tion over a greater area, and thus prevent chafing. 

A strong leather tug, d, is attached to each branch of 
the collar, and at the outer end of the tug is an iron ring, e, 
through which the front trace-chain f passes. 

The trace g is a stout leather strap, terminated at the 
front end by a chain and toggle, f, and at the rear end by a 
ring, through which passes the rear trace-chain h, having at 
one end a hook and at the other end the spring /. The rear 
ends of the trace-chains y, of the swing horses, are attached 
directly to the front trace-chains / of the wheel-horses, thus 
giving a continuous line of traction throughout the teams. 
The loin strap u supports the traces at their middle point. 
The trace-chains of the wheel-horses are attached to the 
single trees i, and in unharnessing, these are detached from 
the double tree, and hooked to the rear of the saddle, for 
which purpose a hook, k, is provided. The spring / is used 
to attach the traces of the wheel-horses to the single trees i. 
This allows a gradual starting of the carriage, and thus 
diminishes the fatigue of the horses, and the strain on the 

Breeching. — This consists of a breech strap m, hip straps 
ss' , two side straps s", and a broad flat strap or martingale, n. 
The breech strap m passes around the hind-quarters of the 
horse, and is supported by the hip straps ss', two on each side. 
The breech strap is joined to the martingale n by the two 
side straps s". The martingale n passes along under the 
horse, and between his forelegs to the front, where it is con- 
nected to a transverse bar, o, on the front end of the pole, 
called the neck yoke. This yoke, o, is of wood, and has a 
ring, /, attached at its middle point, which slips over the 


end of the pole, and rests against a stop, q, on the under 
side. The collars of the wheel-horses are attached to the 
ends of the neck yoke o by the breast straps r. 

In backing, the pressure is exerted by the horse against 
the breech strap m, and this pressure is transmitted through 
the side straps s" and the martingale n, to the neck yoke 0, 
and thence to the pole. 

The action of the harness may be understood from 
Pigs. 220 and 221. For draught and direction t represents 

A A b A 




Fig. 220. 

the traces, j the single trees, d the double tree, b the breast 
straps, c the collar. For breeching b' is the breech strap, 
' m ^S~\ > s * ne s '^ e stra P s > m the martingale, 
n the neck yoke. 

The great advantage of the pres- 
ent harness over the old is the 
change in the breeching, by which 
Fig. 221. the horse has a direct instead of an 

oblique thrust to the rear. Many other improvements are 
embodied in it. 


231. Carriage for Hotchkiss Mountain Gun — For 3.6 Field Mortar. 

Hotchkiss Mountain Carriage (Fig. 222).— The flasks 
a are made of steel strengthened with angle-irons, b, and with 
three transoms, c, d, e, and a trail-plate, g. The axle is solid, 
and the wheels have bronze naves. Recoil is checked when 
necessary, by a rope tied around the spokes of the wheels, 
and passing over the stock. 

The elevating screw passes through the transom e. For 



draught, a pair of shafts is attached to the trail by the hook 
h and a pin, and the gun and carriage drawn by one mule. 
The gun and carriage are generally packed on two mules, 

Fig. 222. 

and the ammunition carried in boxes on mules also. Weight 
of carriage, 220 lbs. The carriage for the 3-inch gun is 
similar to this. 

Fig. 223. 

3.6 Mortar Carriage (Fig. 223). — This carriage is 
made of cast steel, in a single piece, provided with a. clamp- 
ing device in front, which bears against a steel arc attached 
to the mortar. 

Elevation is given by the quadrant, and the mortar 
clamped in position by the clamping device. When in use 
the carriage rests on a wooden platform, and recoil is 
checked by a heavy rope attached to stakes in front. 



232. 3.2-inch Field-gun Carriage. 

This carriage was designed by Colonel Buffington of the 
Ordnance Department. Its principal features are — 

1. The method of reinforcing the axle ; 

2. The formation of the flasks ; 

3. The elevating device ; 

4. The brake. 

Reinforcing Axle. — To stiffen the axle against recoil, 
the body is enclosed (Fig. 224) between two plates of steel, 

Fig. 224. 

which are liveted together temporarily, bored out to a 
diameter slightly less than that of the exterior of the axle 
body, and the plates then riveted tightly together. The 
width of these plates is in the plane of the lower edges of 
the flasks, and hence they resist the force of recoil. They also 
serve as supports for the flasks which are bolted to them. 

Formation of Flasks. — Each flask (Fig. 225) is formed 
of two pieces of sheet steel, stamped while hot between 
dies into the shape shown, and riveted 
together through the flanges. The 
lower edge a of the outer piece of 
each flask projects inward, forming 
N a a/ a/ a flange, to which the transoms are 

Fig. 225. riveted, and by which the flasks are 

bolted to the axle plates. The flasks are connected by 
transoms, three of which form a toul-box, with a hinged lid, 
for carrying tools, oil-can, and loose primers. 

The above construction gives great lateral and vertical 
stiffness. The lower ends of the flasks converge to a trail- 
plate, at the extremity of which is the lunette ring, by which 
the carriage is hooked to the limber. 

Elevating Device. — This is an assemblage of jointed 
levers, previously described, called a " lazy tongs." 



Brake. — The bowspring brake is used. 

Minor Parts. — The wheels are of the Archibald pat- 
tern. The trail handspike is made of two pieces of wood 
split axially, and having a sheet of steel between them, the 
whole bound together by a series of rings. The handspike 
is hinged to the trail-plate, and when not in use is folded 
against the trail, and held in place by a spring catch. 

There are two seats for cannoneers on the axle. The 
flasks also carry the supports for the sponge and rammer, 

The complete gun-carriage is shown in Fig. 226. 

Fig. 226. 
233. The Limber. 

The principal parts of the limber are — 

1. The wheels arid axle ; 

2. The pole ; 

3. The supports for the ammunition-chest ; 

4. The ammunition-chest. 

Wheels and Axle. — The wheels are the same as those 
of the gun-carriage. The axle is of steel, but as it does not 
withstand the shock of recoil, it is not reinforced. 

The Pole. — This consists of two parts, one of which is 
permanently attached to the limber, and is called the fork, 
a (Fig. 227), and the other the pole proper, b. 

The fork is of steel, of this section, ^ ^, and is attached 
to the axle-body. It is prolonged to the rear, and carries 



upon its rear end the pintle-hook c and key d. The pole b 
is made of light elastic wood, and as it may be broken, is 
held in the fork by a bolt, e, and can be readily removed 
and replaced. Its outer end carries a pad, /, to prevent 
injury to the swing-horses, and a stop, g, against which the 
neck yoke rests ; h is the double tree held by a bolt, i. 


■ A n=JH 

Fig. 227. 

Supports for Ammunition-chests. — The ammunition-chest 
/ (Fig. 229) is supported by the fork, and by the two 
hounds k. These hounds are braced to the fork in rear, and 
are connected together in front, and also to the fork, by a 

The hounds not only support the chest, but they 
strengthen all the parts, and assist in transmitting the force 
of traction to the axle. The chest is bolted to the hounds 
front and rear. The hounds and fork also support the foot- 
boards m (Fig. 229), upon which the feet of the cannoneers 

Ammunition-chest. — This is made of wood for lightness. 
It carries the ammunition for the immediate supply of 
the gun, and is of the same size as the chests of the caisson 
for interchangeability. It also furnishes seats for the can- 



The lid opens on top. The advantage of this is that the 
chest can be made waterproof until the water reaches the 
lid. Its disadvantage is that the ammunition is less accessi- 
ble than if the lid opened on the rear side. The advantage 
in case of field artillery outweighs the disadvantage, since 
the cartridges for this service are carried in bags, and hence 
the ammunition would be spoiled by access of water. For 
metallic ammunition, as with machine guns and the revolv- 
ing cannon, as they are not liable to damage by water, the 
lid opens on the side for accessibility. 

The interior of the chest is divided into three parts by 
two partitions (Fig. 228). The projectiles are placed up- 
right in the end divisions a, and the 
cartridges in the middle division b. 
The cartridges are thus in a measure 
protected from fire by the pro- 
jectile. The chest is low, so that a 
Fig. 228. man of ordinary height can easily 

get at the ammunition. 

Each chest carries 42 rounds. To avoid accident, no 
primers are carried in the chest. 

Packages of primers are carried in the cylindrical boxes, 
with screw tops (n, Figs. 227 and 229), and loose primers in 
the tool-box of the gun-carriage. 




Fig. 229. 
The limber complete is shown in Fig. 229. The descrip- 
tions of the caisson, forge and battery wagon, and artillery 


store-wagon, are omitted. The carriage and limber for the 
3.6-inch field-gun resemble those for the 3.2-inch gun. 


234. 5-inch Siege-gun Carriage. 

Fig. 230. 

This carriage (Fig. 230) is made of steel plate \ inch 
thick, the cross-section of the flasks being as shown at A. 

The cheeks are united by two transoms, b, c, in front, and 
connected in rear of c, as shown in figure A. The axle r is 
of steel and hollow. The elevating device is a double 
screw e, connected by a strap d with an axis d', parallel to 
and under the trunnions. The object of the strap has been 

Recoil is checked by a hydraulic buffer, s, which, when 
the gun is in the firing position, is connected by straps / to 
a bolt, g, on the platform. The piston-rod of this buffer is 
attached to the carriage by a lug, k. Figure B shows the 
arrangement of buffer and straps for attachment to bolt on 
platform ; k is the travelling trunnion-bed, only one being 
shown ; / is the lunette plate and lunette. When arranged 
for travelling, the pintle of the limber passes through /, the 
gun is moved back into the travelling trunnion-beds k, the 
hydraulic buffer occupies the position ;;/, and the elevating 



screw the position n. The principal characteristic of the 
carriage is the height of the trunnion-beds, which are 72.25 
inches, or 6 ft. I in. from the ground. This is to enable the 
gun to be fired over a parapet of sufficient height to shelter 
the gunners. 

235. 7-inch Siege-howitzer Carriage. 

This carriage (Fig. 231) is made of steel plate J inch 
thick, the cross-section of the flasks being similar to that of 
the siege carriage. The cheeks are held together by tran- 
soms, and the axle is solid. The carriage differs from the 
5-inch in the following points : 

Fig. 231. 

The cheeks are cut out at ab to decrease the weight. 
The piece is supported on sliding trunnion-pieces, c. In 
front are two hydraulic buffers, d, which limit the recoil of 
the trunnion-pieces c to about six inches. In rear of the 
sliding trunnion-pieces c are two sets of Belleville or spiral 
springs e, which return the piece to its firing position upon 
the carriage. The rod upon which the springs are strung 
passes through a hole, /, in the travelling trunnion beds n. 

The recoil of the carriage is checked by the buffer g, 
attached as in the 5-inch siege-carriage. The elevating 
device consists of a rack, k, bolted to the howitzer, in which 
works a worm, i, mounted between two lugs,y, on the slid- 
ing trunnion-piece c. 



A splined or square shaft, k, passes through this worm 
and its lugs,y', and fits loosely, so that the worm may slide 
along the shaft. When recoil occurs, the trunnion-car- 
riages slide to the rear along the upper surface, in, of the 
cheeks, carrying with them the piece and the elevating- 
gears h and i. The springs e then act to force the gun 
and elevating gear back into position. With this carriage 
the first shock of recoil is taken up by the, upper buffers, d, 
and the strain gradually transmitted to g- The carriage 
can thus be made lighter and stronger. 

236. 7-inch Siege-mortar Carriage. 

Fig. 232. 

h g: 

This carriage (Fig. 232) is made of steel plate as in the 
case of the 5 and 7-inch wheeled carriages, and in its method 
of checking recoil and restoring the piece to the firing posi- 
tion it resembles the 7-inch howitzer carriage. It differs, 
however, in many particulars. 

It is not a wheeled carriage, but is intended to rest upon 
a platform when the piece is fired, like the old smooth-bore 
mortar carriages. Two hydraulic buffers, a, in front, check 
the recoil, while the coiled springs b in rear of the sliding 
trunnion-pieces c, return the piece to the firing position. 
These coiled springs are enclosed in a telescopic or sliding 
case, de, the part d sliding over e in recoil. 


The platform has three traverse-circles,/, bolted to it, 
and also two clamping-circles g. Flanges, h, on the mortar 
carriage fit under these clamping-circles, and retain the car- 
riage in place, preventing its recoil. Lugs, i, are attached to 
the carriage, against which handspikes, j, rest. The lower 
ends of these handspikes are shod, and fit into teeth, k, on 
the clamping-circles. By moving the handspikes, the mor- 
tar carriage may be traversed in azimuth for pointing. 
Elevation is given by a bar, /, which is inserted in radial 
grooves formed in a piece of wrought iron, m, bolted to the 
trunnion. The cheeks are connected by transoms to 
strengthen them, and are cut out at o for lightness. 


237. Classification — Barbette Carriages — Barbette Carriage for 
8-incb. Rifle — Principal Parts — Base-plate — Boilers and 

Classification.— Seacoast carriages are classed into — 

1. Barbette; 

2. Casemate or turret; 

3. Disappearing; 

according as the piece is fired over the parapet; through 
a port or embrasure ; or over the parapet, the gun recoiling 
below it on discharge. 

Barbette Carriages. — The barbette carriages for 8, 10 
and 12-inch guns resemble each other in general, differing 
only in certain details of construction on account of the 
varying weight of the guns. The 8 and 10-inch carriages 
are made principally of cast iron, the 12-inch of cast steel. 
The 8-inch carriage may be taken as a type of the others, 
and will be described. 

Carriage for 8-inch Rifle— Principal Parts. — The 
principal parts of the carriage (Figs. 233 and 234) are: 

1. The base-plate or lower roller path, A ; 

2. The rollers and distance-rings, B ; 

3. The chassis, C; 

4. The top carriage, D. 


Fig. 233. 

="H HP?! J ^TrlHj I I! 


Fig. 234. 



Base-plate. — This consists of a heavy casting, A, shown 
in plan, section, and elevation, Fig. 235. It rests upon a 
bed of concrete, to which it is bolted by the anchor-bolts a ; 
b is the roller-path upon which rests a series of conical 
forged steel rollers, E. The central portion, c, corresponds 
to the pintle in the old carriages, and around it fits a collar, 
d, Fig. 236, upon the chassis, so that rotation in azimuth 
occurs about this central projection. 

Rollers and Distance- rings. — A ring of conical 
forged steel rollers, E, Fig. 235, rests upon the roller-path 

FiOx. 235. 

b of the base-plate, and upon these rests the corresponding 
upper roller-path, c, Fig. 236, of the chassis. These rollers 
are shaped as shown at E, the object of the flange d being 
to keep the rollers in place by its bearing on the inner 
edge of the roller-path. For the 8-inch carriage there 
are twenty of these rollers. They are held in place by 
two distance-rings, B, which are slotted for the axis of the 
rollers as shown at e. The distance-rings are kept in place 
and braced by the braces f. 

338. 8-inch Barbette Carriage — The Chassis. 

This consists (Figs. 234 and 236) of the circular horizon- 
tal part a and the two vertical cheeks b. The circular part, 


a, supports the cheeks, and carries on its lower side the 
upper roller path c, and the central collar d, which fits over 
the corresponding central projection, Fig. 235, in the base- 
plate. The upper surfaces e of the cheeks b are inclined to 
the front, and carry at their forward ends the lugs /which 
hold the piston-rods of the hydraulic buffers. 

In modern carriages, the irregularities due to sliding 
friction are avoided by placing the top carriage on rollers, 
and throwing all the work of checking the recoil upon the 
buffers, which can be very accurately regulated. 

These rollers are shown at £" inserted in recesses in the 

Fig. 236. 

chassis-rail, and rotating on journals, so that the exterior of 
the roller is just above the chassis-rail. 

The device for traversing in azimuth is shown in front 
and in plan in Fig. 234. It consists of a cross-shaft, h, with 
cranks. This shaft carries a worm, i, gearing into a worm- 
wheel, J, which works upon an axis, k, attached to the 

In rear of the worm-wheel is a sprocket-wheel, /, on the 
same shaft withy and attached to it, so that one cannot turn 
independently of the other. A chain, m, is attached at one 
end to the bed-plate at n, and the other end of the chain at a 
corresponding point near the first, not shown in drawing. 

This chain passes under a small wheel in a fork at and 



thence over the sprocket-wheel /. When motion is given 
to / by the shaft, worm, and cranks, the chain will pass over 
the sprocket-wheel and the chassis turn on its rollers, E. 
Vertical motion of the chassis is prevented by clips, x, bolted 
to it and embracing a flange, y, on the bed-plate. 

The device for hoisting the ammunition is shown in rear 
of the chassis. The projectile is run up on a truck (see Fig. 
233), and is then lifted together with the loading-tray by the 
lever/. This lever is on a horizontal shaft, q, which carries 
a worm-gear, r, acted on by the worm s on the shaft /. Its 
action is evident. 

239. 8-inch Barbette Carriage- 
Elevating Device. 

-The Top Carriage and Buffers — 

The Top Carriage and Buffers. — These are shown 
in Fig. 237 in section and elevation. The top carriage 
carries the gun, and consists of a single casting, comprising 
the buffers b, and their connecting transom, a. On the top 
of each buffer is cast the bracket c, carrying the trunnions of 
the gun. 

This top carriage rests on the rollers of the chassis-rail, 
as shown in section, and is held in place, and prevented from 
lifting at discharge, by the flanges d. In the section are also 
shown the ribs or throttling-bars, e, which regulate the flow 
of liquid in the buffers, there being two in each cylinder, 
held in place by bolts passing through the walls of the 
cylinders. The action of these buffers will be explained 
under the subject of Recoil. 

A cross-pipe, /, called an equalizing pipe, connects the 
liquid in the two cylinders, and insures their uniform resist- 



The pistons and rods are removed, by unscrewing the 
nuts, g, which close the rear ends of the cylinders, and then 
by removing the locking and piston nuts h, i, the piston and 
rod can be pushed out to the rear. 

The recoil is limited to 40 inches. 

Elevating Device. — This is shown in Fig. 238. It 
consists of a square shaft, a, attached to the right side of the 
chassis, and working in fixed bearings at b and c ; d is a 
sliding bearing attached to the top carriage. In this bear- 
ing works a bevel-gear, e, gearing into a second bevel-wheel, 
f, on the vertical shaft, g, attached to the top carriage. A 
worm, h, on this shaft gears into the worm-wheel 1, on the 
horizontal shaft j, and on this same sha(t_/ is a second gear- 

Fig. 238. 

wheel, k, engaging with the rack /, on the gun. When recoil 
occurs, the sliding bearing d, moves along the square shaft a, 
carrying with it the bevel-gear e, so that the gears are con- 
stantly engaged, and the gun can be elevated in any posi- 
tion. The return to battery carries the gear e along the 
shaft a. By means of the hand-wheels m and n, the gun may 
be elevated from front or rear. The return of the piece to 
the firing position is due to gravity. Carriages of this kind 
are called gravity return carriages. 

240. The 12-inch Mortar Carriage — General Features — Springs. 
General Features. — This carriage consists of — 

1. The bed-plate or lower roller-path A ; 

2. The rollers and distance-rings B; 

3. The upper roller path or racer C\ 



4. The cheeks D\ 

5. The spiral springs F, and the hydraulic cylinders H. 
The upper roller-path is circular, and supports the cheeks, 

which are vertical, the two together forming the top car- 
riage. The lower roller-path is also circular. 

Springs. — On the side of each cheek is cast a cylindrical 
recess, E (Figs. 239 and 240), which contains a column of 
spiral springs, F. 

These springs are in ten separate lengths, and each 
length is composed of two coils, an inner one, F', and an 

Fig. 239. 

outer one, F. A pile of Belleville springs, F", forms the 
upper end of the column, and upon these the mortar is 
supported as follows : The trunnion-carriage G, of cast steel, 
has a projecting lug, g', through which passes the adjusting 
screw K. 

The lower end of this screw bears on the Belleville 
springs, and by means of it the trunnion carnages may be 
adjusted till the mortar is in the proper position for loading, 
and it is then secured in that position by the jam-nuts k'. 

The trunnion-carriages G, are two heavy blocks of cast 
steel, in which the trunnions rest, and which slide, under the 



H — 

force of recoil, along ways planed on the inner side of the 
•cylindrical recess E\ a slot, m, Fig. 241, being left in the 

recess for the projecting lug g'\ 
„J£ a section of the trunnion-carriage 

-,t and recess is shown in Fig. 241. 
__ _.. The object of the spiral springs 
is to return the mortar to the fir- 
ing position. They are set at an 
"F angle of 50 with the horizontal, 
the mortar being fired between 
.Q the limits 35° and 65 , so that this 
is a mean between them. To ob- 
tain a column of springs of suf- 
ficient length to return the piece 
—E to its proper position, the cylin. 
drical recesses in the cheeks are 
lengthened by bolting a cylinder 
E', Figs. 239 and 240, to the bot- 
ttf torn of E. 

241. The 12-inch Mortar Carriage — 
Hydraulic Buffers. 

Recoil is checked by two 
hydraulic buffers, H, Figs. 239 and 
240, one on each side of the car- 
riage, bolted to the flanges of the 
cylindrical recesses E. The pis- 
ton-rods h' , Figs. 240 and 242, of 
"*» these cylinders are attached to 
the lower ends of the trunnion- 
carriages G. When the piece is 



Fig. 240. 

Fig. 241. 



fired, the spiral springs return it to the firing position, and 

hence this is a spring-return carriage. 

The arrangement of the hydraulic buffer for checking 
recoil and maintaining a constant resist- 
ance in the cylinder, differs from that 
for the 8, 10, and 12-inch guns as fol- 

A channel, A, Fig. 242, is bored 
parallel to the axis of the cylinder H. 
Holes, a, are bored at different intervals 
along this channel, and are partially or 
entirely closed by screw-plugs, b, fitting 
into the holes c. These plugs, b, are of 
different shapes, so that they will either 
completely close the openings a, when 
screwed home, or will leave them par- 
tially or entirely open. They are never 
entirely removed. When the gun re- 
coils, the piston moves in the direction 
of the arrow, Fig. 242. At the first 
instant of recoil, if all the holes a are 
open, it is evident that the liquid will be 
forced freely through these holes, and 
will flow along the channel A, and return 
above the piston, into the cylinder. As 
the motion of the piston continues, each 
of these holes will, in succession, be cut 
off, and the flow of the liquid being thus 
limited, its resistance will increase. By 

partially or entirely closing the holes a, it is evident that 

any resistance to flow, within limits, may be obtained. An 

equalizing-pipe,/, connects the two cylinders, to keep the 

pressure the same in both. 

The piston-rod h' , passes through the cylinder at both 

ends, to equalize the volumes, and the piston-head, s, is 


Its upper side is of the shape shown, and the upper 

cylinder-head, s', is correspondingly shaped. When the 

springs return the piece to the firing position, the head of 

Fig. 242. 



the cylinder,/, enters the recess in the piston-head, s, and by 
gradually forcing out the liquid, the counter-recoil is 
checked, and the piece comes into the firing position 
without shock. Buffers, b, Fig. 240, on the trunnion-car- 
riage also avoid this. 

242. Remaining Parts of the 12-inch Mortar Carriage — Roller- 
paths — Elevating-gear — Traversing-gear — Loading-scoop. 

Roller-PATHS. — In the 8, 10, and 12-inch carriages, 
horizontal motion of the parts is prevented by the central 
collar or pivot, as explained. In the 12-inch 
mortar carriage, as the recoil of the piece is 
downward, the central part of the carriage 
must be left open, and hence the central collar 
cannot be used. Resistance to horizontal 
motion is therefore obtained by forming the 
upper roller-path, C, so that it overlaps the 
lower one, A, as shown in Fig. 243, which is a Fig. 243. 
section of the two. Vertical motion is prevented by the 
weight of the system. 

Elevating-gear. — This consists of a bronze toothed 
sector, a, bolted to the mortar, con- 
centric with the axis of the trun- 
nions, into which works a gear, b. 
A large gear, c, on the same shaft is 
driven by the gear d, and on the same 
shaft with d is a hand-wheel, e. 

The gears b, c, d, and the 
hand-wheel, e, are all mounted on 
the trunnion-carriage, G, and as the 
mortar is mounted on the same FlG - 244 - 

carriage, the whole elevating device recoils together. Each 
trunnion-carriage carries its own elevating-gear. 

Traversing-gear. — This consists of a vertical shaft, a, 
Fig. 245, attached to the upper carriage, carrying a gear, 
b, at its lower end, and a worm-wheel, c, at its upper 
end. The wheel, b, gears into a toothed ring, d, on the 




inside of the lower roller-path, and the shaft is rotated by a 
worm, e, driven by cranks, /, on a horizontal shaft, g, passing 
through the front of the cheeks of the 
-g' top carriage. This device is also shown in 
Fig. 239. 

For pointing in azimuth, a cast-iron 
circle, graduated in degrees, is fixed 
around the upper roller-path, and a pointer 
attached to this path, indicates the direc- 

LOADING-SCOOP. — This consists of a 
scoop or tray, a, Fig. 239, at the end of a 
lever, b. This lever is pivoted to the rear 
of the chassis on a shaft, c, which carries 
also the bent lever d. The outer end of 
this lever carries a nut, e, in which works 
the screw,/. This screw is supported in 
bearings on the left side of the top carriage, and extends to 
the front, where it ends in a hand- wheel, g. By turning this 
hand-wheel, the scoop is raised or lowered, carrying the 
projectile and charge to the breech of the mortar. 

The loading position for the mortar is an elevation of 5°. 

243. Casemate or Turret Carriages — General Principles— Disappear- 
ing Carriages — General Principles. 

General Principles of Turret Carriages. — The 
general object of these carriages, is to secure a minimum 
height, and minimum embrasure opening. Hence the cen- 
tre of rotation is at the centre of the embrasure, and the 
chassis is simply a pair of rails, which support the buffers 
carrying the gun. 

Elevation is given by lowering or raising the rear ends 
of the rails, and direction by rotating the turret. None of 
these carriages have as yet been designed for the land 

General Principles of Disappearing Carriages.— 
Owing to the great cost of modern guns and carriages, it is 
important to protect them as much as possible from injury 
from fire. This may be done either by placing them in 


armored casemates or turrets, or in gun-lifts, or by using 
the ordinary barbette battery, and placing the gun upon a 
disappearing carriage. The great cost and confined space 
of the casemates, turrets, and gun-lifts, has caused the adop- 
tion of the disappearing type of carriages in exposed sites. 

The object of a disappearing carriage is, to enable the 
gun to be fired over an ordinary parapet, thus giving it all 
the advantages of an extensive field of view and of fire, 
with room for manoeuvre, and to utilize the force of recoil 
in returning the gun to cover for loading, and in storing up 
sufficient energy, during recoil, to return the gun to the firing 

There are therefore two points to be especially con- 
sidered : 

1. The means of checking recoil, so that the gun will be 
covered during loading. 

2. The method of storing up energy sufficient to return 
the piece to the firing position. 

Checking Recoil. — In all these carriages, the gun is 
mounted at the ends of lever-arms, and these arms are 
pivoted, in various ways, to the chassis. The recoil is 
checked by hydraulic buffers, or in some cases by pneu- 
matic buffers, which allow the lever-arms to rotate grad- 
ually to the rear, bringing the gun down to the loading 

Return to Firing Position. — The energy necessary to 
return the gun to the firing position, is stored up in various 
ways. In the English service, a hydro-pneumatic buffer 
is used ; that is, the liquid which is forced out of the 
hydraulic cylinder, by recoil, passes into an air-chamber, 
and compresses the air sufficiently, to give the necessary 
pressure for returning the gun to the firing position, as soon 
as a valve is opened between the air-chamber and the 
hydraulic cylinder. 

Spiral or Belleville springs are also employed. The 
recoil is checked by the hydraulic buffer, and the springs 
restore the piece to its firing position. 

Counterweights may be used, either alone, or in connec- 
tion with air pressure. 



244. Buffington-Crozier Disappearing Carriage. 

Two successful carriages of this type have been tried in 
the United States, and an outline description of each will be 

Buffington-Crozier. — This carriage was designed by 
Colonel Buffington, and modified by Captain Crozier, both 
of the U. S. Ordnance Department. 

The carriage consists of the chassis, A, Fig. 246, the sup- 
porting levers, B, carrying the gun, the hydraulic buffers, C, 
and the counterweight, D. The carriage is a front-pintle 
one. The gun is mounted on the upper ends of the support- 

FlG. 246. 

ing levers, B. These levers have trunnions, e, near the mid- 
dle, which are mounted on the hydraulic buffers, C. The 
lower ends of the levers are connected by a cross-head at /, 
and from this cross-head, is suspended the counterweight, 
D. This counterweight rises and falls vertically, while the 
trunnions, e, with the buffers, move horizontally along the 
chassis-rail, a. When the piece is fired, the force of recoil is 
taken up by the buffers, which move back as stated, while 
the counterweight, D, is raised vertically, sliding on guides, 
g. The gun in the loading position is shown at G. The 
counterweight is held in its position after firing, ^y a pawl, 



h, and ratchet, i, which being released, allows the weight to 
descend, and thus the gun is raised to the firing position. 
The trunnions of the gun describe an arc of an ellipse in 
their descent. The bars E are for giving elevation. They 
are attached to a straight rack, b, on the inside of the chassis, 
which is worked by the hand- wheel c. The elevation may 
be given in either the loading or the firing position. The 
carriage rests in front upon a ring of rollers, F, as previously 
described, and is traversed by the chain, d, passing over a 
sprocket-wheel, and worked by a crank. 

245. The Gordon Disappearing Carriage. 

Fig. 247. 

Fig. 248. 

This carriage was designed by Capt. Gordon of the 
U. S. Ordnance Department, and consists (Figs. 247 and 
248) of the chassis a, the top carriage b, the counterpoise c, 
the lever-arms d, the hydraulic cylinders <?, and the air- 
chamber f. 

The chassis, a, is a heavy casting, supporting all the parts, 
and it rests when in the firing position upon a platform. 
When the> piece is to be moved in azimuth, the chassis is 
supported on a hydraulic pivot, not shown in the drawings, 



by which arrangement the traversing is effected with very 
little power. 

Oii the upper side of the chassis, four levers, d, are 
mounted, two of them being shown in the drawing. 

These levers rotate about the axes, g, and carry at their 
lower ends, a heavy counterweight, c. On the upper ends 
of these levers is mounted the top carriage, b, which sup- 
ports the piece. A hydraulic cylinder, e, extends along the 

Its piston is forced in, during recoil, and the liquid, thus 
forced into the air-chamber f, compresses the air, and 
stores up the energy necessary to return the piece to the 
firing position, when the proper valve in the air-chamber 
is opened. The trunnions describe an arc of about \$>o a 
during recoil, thus bringing the gun close to the parapet, 
and affording good cover. The elevating device is attached 
to the top carriage. This is a centre-pintle carriage. 

Several disappearing carriages are in use abroad, as the 
Moncreiff, Armstrong, Canet, etc. 

246. Old Seacoast Carriages in TJ. S. Service. 

Certain old carriages are still retained in the U. S. ser- 
vice for the 8-inch converted rifles, and the 15-inch Rodman 
smooth-bore guns. They consist (Fig. 249) of a chassis, a t 
and a top carriage, b, made of wrought iron. 

Fig. 249. 


The chassis is composed of two parallel, I-shaped rails, 
connected by transoms, and attached to it, between the rails, 
is the hydraulic buffer, c. The piston of this buffer is at- 
tached to the top carriage by a lug, d, on the latter. The 
buffer itself,.is one of constant orifice, and variable resistance, 
as will be explained. Bolted to the rear end of the chassis- 
rail, is an inclined rail, e. The retraction gear is shown at/. 
The principle of this carriage is as follows : 
When the piece is fired, the top carriage rests, through- 
out its length, upon the chassis-rail, and hence the force of 
recoil is distributed over this length, and the top carriage 
starts to the rear on sliding friction. After a very small 
movement in recoil, the wheel, g, of the top carriage (Fig.250), 
strikes the wedge-shape drail, e, and begins to rotate. This 
causes the top carriage to tip slightly forward, and brings 

Fig. 250. 

the front wheel, h, into bearing on the chassis-rail. The car- 
riage then moves on rolling friction. The result of this 
arrangement is, that the top carriage rests, throughout the 
recoil, on rolling friction, as shown Fig. 250. A spring pawl 
and ratchet, retain the top carriage in the loading position, 
after recoil, and by releasing the pawl, the top carriage 
returns on rolling friction to its firing position, by gravity. 

For drill purposes, to bring the gun from battery, for 
loading, the rear wheel, g, is mounted on an eccentric axle, 
and when thrown into bearing against the chassis-rail, by the 
action of a handspike, it tips the top carriage forward, and 
brings the front wheel, h, also into bearing. The piece, and 
top carriage, are then drawn to the rear, by a rope attached 
to the latter (Fig. 249), and wound round a drum on the shaft 
of the retraction gear/. 



247. Maximum Velocity of Recoil. 

The velocity of recoil at the instant the projectile leaves 
the muzzle is given by equation 65, Interior Ballistics. This 
does not represent the maximum velocity of recoil, however, 
for the reasons stated, and a new equation is necessary to 
determine this velocity. 

In equation 65, it is assumed, that the mean velocity of 
the particles of the charge, is one half that of the velocity of 

the projectile; that is, the equation contains the termf— v), 

in which w is the weight of the charge, and v the velocity of 
the projectile. 

This is very nearly true while the projectile is in the 
bore, because the layer of gas next the projectile has the 
same velocity as the latter, and this velocity decreases to 
zero, for the layers toward the bottom of the bore. 

But when the projectile leaves the muzzle, this condition 
no longer exists. The gases, which were before confined, 
rush out with greatly increased velocity, and this affects 
the recoil of the piece. 

Let P denote the weight of gun, and part of the carriage 
which recoils ; 
p, the weight of the projectile ; 
do, the weight of the charge ; 
VJ, the maximum velocity of recoil ; 
V, the initial velocity of the projectile ; 
v n , the mean of the maximum velocities of the powder- 
gas upon issuing from the piece. 
Then the equation 

PV m '=fiV+<Sv m (335) 

expresses the equality of momenta of the piece, projectile, 
and charge at this instant. 

General Sebert of the French Artillery, has determined 
with his velocimeter, previously described, that in order that 
the above equation be true, the value v m must be about 3000 
ft -sees. 


Hence the maximum velocity of recoil is given by 

VJ=?Z±f?™ (336) 

while the velocity of recoil during the time the projectile is 
in the bore is (equation 65) 

pv -\- —v 
r ' 2 

v = ■ 


248. Periods of Recoil— Relation between Time, Velocity, and 
length of Recoil in First Period. 

Periods. — The recoil of a gun is divided into two 
periods : 

1. From the time the gas begins to act, until the maximum 
velocity of recoil is attained. 

2. From the end of the first period, till the piece is 
brought to rest. 

Relations between Time, Velocity, and Length of 
Recoil in First Period. — In order to determine the cir- 
cumstances of recoil in the first period, it is necessary to 
know the relations between the time, velocity, and length of 
recoil, and these are determined in the following manner : 

If the distance recoiled by the piece, at the end of any 
time t, be denoted by x, the velocity at that time is 


and the distance x passed over is 

x = J v 'dt. 

Hence; considering the expression / v'dt, if we con- 
struct a curve whose abscissas are the values of t, and whose 
ordinates are the corresponding values of v', this curve 
will be of the form Fig. 251, and from it we deduce the fol- 
lowing laws : 

1. The velocities of recoil increase very rapidly at first, 
till the point of inflection i is reached, and then more slowly, 



till they cease to increase at the time corresponding to the 
maximum velocity V m ', which time is denoted by r. 

2. The area included between the curve, the axis T, and 
any ordinate v ', is the distance x passed over in recoil, at 

the time t corresponding to that ordinate, since x — I v'dt; 

and the total length of recoil during the first period is the 
area corresponding to the ordinate t. 

This curve was constructed by experiment, by obtaining 
with the Sebert velocimeter, the values of v ' corresponding 
to different values of t. 

Fig. 251. 

249. Ordinary Case — Steps in the Solution of the Problem. 

In the case just considered, the relations between the 
velocities of recoil v ', and the corresponding times t, were 
determined by experiment. 

Ordinary Case. — Ordinarily, this relation between v' 
and t is not known. It may, however, be determined by a 
series of steps as follows : 

Steps. — We have the relation between the velocity of 
the projectile v and the length of its travel u in the bore, 
by.Sarrau's monomial or binomial formulas; hence we have 
a relation v =/(u). 

1. We next determine the time t required for the projec- 
tile to pass over any length of bore u. This gives a relation 
t = f(u). 



: f{u) and t =f(u), we de- 

2. Combining the curves v 
termine the relation v =/{(). 

This is done by using the ordinates of the time curve 
/ = f{u) as abscissas, and those of the velocity curve v — /(«) 
as ordinates, and constructing a curve whose equation is 
v—f(f). This equation gives the relation between the 
velocity of the projectile, and the corresponding time t. 

3. To pass from this curve to that of the velocity of re- 
coil as a function of the time t, we have equations (65) and 
(336), giving the relation at any time t between the velocity 
of the projectile and that of the piece; and knowing that of the 
projectile we may at once find that of the piece as a function 
of the time, or v' =f(t), which is the curve required. 

Fig. 2C2. 

Having the curve v' = /(/), we can determine, as pre- 
viously shown, the time, and length of recoil, corresponding 
to any given velocity. 

250. First Step — Time of Passage of Projectile over a Given Length 
of Bore — Difficulty — Remedy. 

Assuming the binomial and monomial formulas (91) and 
(121), Interior Ballistics, we apply the one which is suitable 
to the particular case under consideration, and construct 
the curve whose abscissas are the values of u, and its ordi- 
nates the corresponding values of v. This curve will be of 
the form Fig. 252. 

The value for the velocity at any point u is, from calculus, 


v = 



from which we have 

i__ dl 
v du 

Multiplying by du and integrating, we have 
I —du = / -j- du = I at = t, 





Fjg. 253. 

Hence if we construct a curve whose abscissas are the 

values of u, and its ordinates the corresponding values of — , 

the area included between this curve, the axis of u, and any 

ordinate — will give for any value of u the time t required 

for the projectile to pass over this distance u in the bore. 
The form of this curve is shown in Fig. 253. 
Difficulty. — The only difficulty in this case is that for 

very small values of v the ordinates — will be large, and will 

not fall within the limits of an ordinary drawing, and hence 
the area under the curve cannot be accurately measured, 



and therefore the time corresponding to a given travel u 
cannot be exactly ascertained. 

Remedy. — To obviate this difficulty, we assume (as is 
nearly correct) that the velocity of the projectile, as a 
function of the time varies nearly as the abscissas and 
ordinates of a common parabola, whence we have 

v = Jzpt. (337) 

Multiplying by dt and integrating, we have 

J vdt = / -^dt =u = / ^2ptdt = f(2/)M. (338) 

Fig. 254. 

At the instant the shot leaves the bore, v in equation 
(337) becomes the initial velocity V. Denoting the cor- 
responding time by t', we have, equation (337), 

and this value of y 2/ in equation (338) gives 

t' = 

3 « 

2 y (339) 

being the total length of travel of the projectile. Com- 



paring this total time of passage of the projectile through the 
bore, with that obtained from that part of the area under the 
curve of reciprocals which can be measured, the value of 
the unmeasured portion can be ascertained very nearly. 
Thus the relation t = /(«) is determined and the curve is 
given in Fig. 254. 

251. Second and Third Steps in Determining the Curve of Velocity 
of Recoil as a Function of the Time. 

Second Step. — Taking the ordinates of the curve 
t = f(u) as abscissas, and those of the velocity-curve 
v =f(u) as ordinates, we construct a curve v = f(t), showing 
the relations between the velocity of the projectile and the 
corresponding time, and this curve will be of the form 
shown in Fig. 255. 

Fig. 255. 

Third Step — Relation between Velocity of Pro- 
jectile and THAT of Recoil. — We have for the velocity 
of recoil of the piece and carriage while the projectile is in 
the bore, equation (65), 

'p + 

and for the maximum velocity of recoil, equation (336), 
r ^_- ? F +3ooo<3 

* 111 7~* • 



Since v is determined as a function of t by the second 
step, v' may be found for the corresponding times by 
equation (65), by multiplying the ordinates of the curve just 

determined, Fig. 255, by the ratiol _ J. A curve can 

then be constructed, similar to that in Fig. 255, giving the 
velocities of recoil of the piece, for each instant of the 
passage of the projectile through the bore, and the area 
under this curve, bounded by the axis of T and any 
ordinate v' will give the corresponding space passed over, 

since I v'dt = x. 

After the projectile quits the bore, equation (65) no 
longer applies; but it is known that the curve becomes 
tangent to a line parallel to the axis of T, at a point given 

Fig. 256. 

by equation (336), and it is reasonable to infer, that the rate 
of curvature of the curve of recoil, will continue uniform up 
to this point of tangency. 

Hence, drawing a line parallel to the axis of T, at the 
distance given by equation (336), 

V ' = 

pV '+ 3000C0 

and continuing the curve already drawn, preserving its gen- 
eral rate of curvatu're up to this line, we have the curve 



v' = fit), giving the time and space passed over in recoil, 
and this curve will be of the form Fig. 256. 

252. Example — 8-inch Steel B. L. Rifle— First Step— Curve t —f{u). 

For example take the case of the 8-inch Steel B. L. Rifle. 
The velocity curve for this gun, with 125 pounds brown 
powder, is given in Fig. 257. 

Fig. 257 

From it we obtain the following abscissas and ordinates : 

a (Feet). v (Foot-seconds). 

O.46 387 

1.70.... 935 

2.4O IO80 

320 1 197 

3-70 1259 

7-30 1545 

95° l6 55 

11.50 1727 

13-00 ,. 1787 

14-30 1827 

15-75 1859 

17.43 1884 I. V. 

From which we have the following values of — , and the 
curve of reciprocals, Fig. 258. 



« (Feet). i. 


O.46 OO2584 

I.70 OOI069 

2.4O OOO9259 

3.20 OOO8354 

3-7° OOO7943 

7.3O OOO6472 

9.5O OOO6042 

H.50 OOO579O 

1 3.00 0005 596 

14-3° OOO5473 

15-75 OOO5379 

17-43 OOO5308 



Fig. 258. 

For the total time of passage of the projectile through 
the bore we have, using the area of the parabola (eq. 339), 

zV 2 1884 

.01387 sec. 

Hence the total area under the curve of reciprocals 
should be nearly .01387 second. 

In the absence of a more accurate method, the area under 
the curve, which can be measured, may be obtained by con- 
sidering each portion of the area bounded by the curve, the 



axis of u, and the two adjacent ordinates, as a trapezoid, and 
finding its area. 

Thus for the first trapezoid we have 

ordinates \ ' , 
( .001069 

Value of u = 1.24 = 1.70 — 0.46. 

. /.002584 4- .001069^ w 
Area I J ' -I X 1.24 = .00227 sec. 

Following this method, we have the table : 

« (Feet) 















Successive times, 

Total times, 


.00227 00227 

.OO06979 0029679 

.OOO704 OO36719 

.OOO4075 OO40794 

.OO2592 O066714 

.OOI386 OO80574 

.OOllSo OO92374 

.OOO854 OIOO914 

.OOO715 OIO8064 

.OOO787 OI 1 5934 

.000897 o 1 24904 

From this table we can obtain the time of travel of the 
projectile over any distance u. 

The sum of the times is .01249 second, while the total 
time is, as above shown, .01387 second. 

Hence the difference, .00138 second, is the area that can^ 
not be measured. 

253. Examples — Second and Third Steps. 

The table on page 442 gives the curve v = flu), that on 
this page the curve t — f{u). Taking the ordinates of the 
latter curve as abscissas, and those of the former as ordi- 
nates, we can form the following table, whose abscissas and 
ordinates are those of the curve v =f(t) : 


Total Successive times, Ordinates. 

times, /. seconds. Velocities foot-seconds, v. 

O O 

.OOI38 OOI38 387 

.00365 00227 935 

.0043 5 000698 1080 

.00505 000704 1 197 

.00546 0004075 1259 

.00805 002592 1 545 

.00944 001386 1655 

.01062 001 1 80 1727 

.01147 000854 1787 

.01219 000715 1827 

.01297 000787 1859 

.01387 000897 1884 I. V., 

and from this we construct the curve of velocities of the 
projectile as a function of the times. Passing to the consid- 
eration of the recoil of the piece and carriage, we have, 
equation (65), 



v = —rp—v. 

p = 300 lbs. ; 
<3 = 125 lbs. ; 
P — 18 tons = 40320 lbs. 

v' = .008992; = .009^. 

From this formula, having the values of v and the corre- 
sponding times t, we can form the following table and con- 
struct the curve of recoil of the piece and carriage as a 
function of the time. 

Velocity of recoil of 
Total times, Piece and Carriage, 

seconds. foot-seconds. 


.OOI38 3.483 

■OO365 8.415 

•OO435 9720 

.00505 I0.773 


.OO546 II.33I 

.OO80S I3-905 

.00944 I4895 

.OI062 I5.56l 

.OI I47 16.083 

.OI219 16.453 

.OI297 16.731 

.OI387 16.956 

From equation (336) the maximum velocity of recoil is 

" m p > 

V m ' = 23.32 ft.-seconds. 





H- .01387- 

Fig. 259. 

From the above data the curve of recoil, Fig. 259, may 
be constructed. 

Drawing a line parallel to the axis of T, at the distance 
VJ = 23.32 ft.-secs., this line will mark the limit of accelera- 

From this curve, the time corresponding to any velocity 
of recoil can be obtained, and the area under the curve will 
give the corresponding space passed over. 

254. Problems. 

1. Required the time at which the velocity of recoil is 
13.905 ft.-sec. 


The table page 446 shows it to be .00805 second. 

2. Required the space passed over in recoil at the end of 
this time. 

It will be the area under the curve, from the origin, up 
to the ordinate whose value is 13.905 ft.-secs., or, approxi- 
mately, the sums obtained by adding the separate areas 
regarded as trapezoids, up to this point. As an approxima- 
tion to the true result, regard the curve as a parabola. The 
result thus obtained will be slightly too great. The area 
under the curve will be two thirds the rectangle of the ab- 
scissa and ordinate of any point. 

Hence for the area in question we have 

s = - X .00805 X 13-905 = -0746 ft. = .895 inches. 

3. Required the space passed over by the gun and car- 
riage at the time the projectile leaves the bore. 

By the same method of approximation we have 

s = - X -01387 X 16.956 = .1567 ft. = 1.88 inches. 

4. Required the time at which the velocity of recoil is a 
maximum, and the space passed over at this time. 

The curve v =f{t) gives, by measurement, for the value 
of t = .0395 seconds. 

The space passed over will be approximately 

s = - X .0359 X 23.32 = .558 ft. = 6.70 inches. 

In the same way all the circumstances of the recoil of a 
gun during the first period, may be obtained, having the 
curve v — f(u), which can be obtained from Sarrau's 

255. Time and Length of Recoil in Second Period. 

Time of Recoil. — At the beginning of the second 
period, the acceleration is zero, and the gun and carriage 
have acquired the maximum velocity of recoil VJ. For 
simplicity of discussion, suppose the chassis horizontal. 


The only force acting during the second period is friction, 
and this being practically constant, will uniformly retard 
the carriage and piece, till they are brought to rest. 
Let/ be the coefficient of friction = 0.2 about; 
y the retardation due to friction; 
P the weight of the gun and carriage which is mov- 
ing in recoil ; 
M the mass of the moving parts ; 
V" the velocity of recoil at any time t during the 
second period. 
Then from mechanics 

dV" fP 
r = -^T=~M (34o) 

The velocity at any time t during the second period will 
be, from (340), 

f dV " = /-§*=-!? + * ■ ' (340 

When t = o, or at the beginning of the second period, 
V" = VJ ; hence in (341) we have 

V " =V "'-'M t - (342) 

At the end of the second period, when recoil ceases, 
V" = o, and the corresponding time is, from (342), 

MV ' V ' 

T -yp-=~F (343> 

Length of Recoil. — Assuming equation (342), we have 
for the length of recoil, at the end of any time, t, in the second 

dt v m M ' 

jds^Jv"dt^Jv n dt-j f -^tdt. . (344) 


• • • • (345) 

At the end of recoil we have for the value of t, from (343). 


<= v -'-¥ii f - 



Substituting this value of t in (345) gives 



hence in (346) 

g f 2 M gT 

f -=gf- 
M gJ ' 

V m 




Fig. 260. 

256. Curve Representing Total Recoil — Application to 8-inch Rifle. 
Second Period. 

Curve of Total Recoil. — The curve representing all 
the circumstances of recoil of the piece and carriage, will be 
obtained, by combining that for the first period, with the 
right line representing the second period, and will be of the 
form Fig. 260. 

Application to 8-inch Rifle. 

1. Required tHe time, from the beginning of the second 
period, at which the velocity of recoil will be 10 ft.-secs., 
and the space passed over at that time . 

From (342), 

10 = 23.32 — .2 X 32.2 X t; 


t = 2.068 seconds ; 
from (345), 

s — 23.32 X 2.068 - i X .2 X 322 X (2.o68) s ; 
> s — 34.46 feet. 

2. Required the time from the beginning of the second 
period to the end Of recoil, and the total space. passed over 
in recoil : 

From (343), 

23.32 • , , 

t = — = 3.621 seconds. 

32.2 x .2 

From (347), 


42.22 feet. 

2 x 32-2 X .2 

In a similar manner, all the circumstances of the recoil 
during the second period can be obtained, having the value 
of VJ from formula (336). 

257. Wheeled Carriages — Cases. 

The preceding discussions relate to carriages which slide 
in recoil, such as those for seacoast guns. 
\ For wheeled carriages two cases may arise : 

1. The carriage may recoil, the wheels rotating, and not 
leaving the ground or platform upon which they rest. 

2. The wheels may leave the ground or platform, depend- 
ing upon the relative values of the components of the force 
of recoil which act to produce translation and rotation. 

In the second case, the phenomenon of recoil is composed 
of alternate periods, during which the wheels rise, and return 
again to the platform. 

If the carriage slides in recoil, with the wheels always in 
contact with the ground, the preceding discussions apply, 
the only change necessary being a decrease in the value of 
the coefficient of friction, due to the lubrication of the bear- 
ing surfaces of the nave and axle-arm. The coefficient, /, in 
this case is decreased to about two thirds its ordinary value. 

If the wheels rise, increased pressure is produced on the 
trail. This increased pressure, decreases the extent of recoil 



as compared with that which obtains in the first case, and hence 
the values for time, velocity, and length of recoil deduced for 
the first case, will be greater than those for the second. As the 
calculations in the second case are somewhat complicated, 
those for the first case may be used instead of them, as being 
safe in practice. 

258, To Calculate the Angle of Elevation of the Piece for which the 
Wheels will Rise. 

The rotation of the carriage about the trail, depends on 
the angle of elevation at which the piece is fired. There is 
a limiting angle for which this rotation will occur. For all 


^V^—- -~_ "'; ? 1 




• 7 ^-\> 


) t 

r c 

Fig. 261. 

angles greater than this, rotation will not occur, and for all 
angles less than this, it will always occur. It is required to 
determine this limiting angle. 

Let OM, Fig. 261^ be the axis of the piece, and the line 
of action of the force P . Resolving this force into its com- 
ponents parallel and perpendicular to the ground, we have 

OE = P cos a ; 
ON — P t sin a. 

With reference to the point C, the component OE acts 
with a lever-arm OD to raise the wheels, while ON acts 
with a lever-arm DC to keep them in contact with the 


ground. Let G be the centre of gravity of the system, 
composed of gun and carriage. 

Then the weight P acts at G, with a lever-arm CI, to 
keep the wheels down. In addition to these, the system 
moves under the action of the force OE with an accelera- 
tion y, and hence its force is My, and this force diminishes 
the rotative effect of the force OE, since the action of 
this force OE, is to produce both rotation around C, and 
translation along CD. 

This latter force, My, has a lever-arm GI. We have 
therefore, calling those forces which tend to cause a lifting 
of the wheels positive, and those which oppose it negative,. 

-\- OE, lever-arm OD ; 

- ON, " DC; 

- P, " CI; 

- My, " GI. 

When the sum of the moments of these forces with 
respect to C is zero, the wheels will be on the point of 
leaving the ground. 

Hence this gives the condition required. 

OD — a, 

DC = d, 



we have 

+ P„ cos a . a — .P sin a . d — P . b — Myh = o. (348) 

The value of y is obtained as follows: Denoting the 
total pressure of the powder-gas by P a , the component of 
this pressure causing recoil is P cos a. This force is opposed 
by the friction due to the component P sin a and the weight 
of the gun and carriage P. Hence the force opposing 
motion is f(P sin a -4- P). 

From mechanics we have therefore for the acceleration 

y = jf[P c cos a -f(P a sm a + P)]. . . (349) 


Substituting this value for y in (348), which can be done, 
rsince the wheels are just about to leave the ground, and 
therefore the case is one of horizontal sliding, we have 

P a cos a(a - k) — P sin a{d — fti) — P(b — fh) — o. (350) 

Now making P—o in comparison with P a , and calling 
«„ the value of a for this limit, where the wheels are just 
quitting the ground, we have 

tan "o=J^ (350 

in which a and d can be found by direct measurement of 
the gun and carriage, and the centre of gravity by suspend- 
ing the system in two different positions, and noting the 
point of intersection of the lines of suspension when pro- 


259. Necessity for Means of Checking Recoil — Conditions which a 
Good Brake should Fulfil — Classes. 

Necessity for Means of Checking Recoil. — The 
above discussion, and its application in the case of the 8-inch 
gun, show, that unless some artificial means be employed 
to check recoil, its extent will be so great as to cause 

This is especially true with modern field, siege, and 
seacoast guns, where the weights and initial velocities of 
the projectiles have greatly increased, without a correspond- 
ing increase in the weight of gun and carriage, and hence 
the length of recoil has been greatly increased. 

In the field and siege services, this entails great fatigue 
upon the cannoneers in running the gun and carriage back 
to battery, with a consequent delay in firing, and exposure 
to the enemy's fire. 

In the seacoast service, the length of recoil must be 
limited to three or four calibres, on account of cover, as the 
guns, if mounted in turrets, or similar places, have very lim- 
ited space for working; and if mounted in barbette, a long 


recoil exposes the gun to hostile fire, and increases the time- 
between shots. For these reasons, brakes or buffers are 
employed with modern guns. 

Conditions which a Good Brake should Fulfil. — 
A good brake or buffer should fulfil the following conditions : 

i. Its resistance should be constant at all times. 

2. For the same piece, charge, and projectile, the length 
of recoil should always be the same, which is a proof of the 
regularity of its action. 

3. It should be entirely automatic. 

4. Its line of resistance should be as nearly as possible in 
the line of action of the force producing recoil, so as to avoid 
an overturning moment; and it must not interfere with the 
movement of the gun to and from battery, and its manoeu- 

Classes. — Brakes are divided into two general classes : 

1. Friction brakes. 

2. Hydraulic brakes. 

260. Friction Brakes for Seacoast Carriages — Objections. 

The various friction-brakes for field and siege carriages,, 
have already been explained. Those for seacoast carriages 
consist generally of a series of plates, fixed to the chassis, 
between each pair of which, slides a plate attached to the 
top carriage. The plates are so arranged, that by means of 
a screw or other device they may be pressed together, and 
the friction due to this pressure limits the recoil. 

Let P, represent the pressure at each surface in contact ; 
n, the number of surfaces ; 
S, the length of recoil in second period ; 
/, the coefficient of friction ; 
P, the weight of gun and carriage recoiling ; 
VJ, the maximum velocity of recoil with brake acting. 
Suppose the chassis horizontal ; then the work of fric- 
tion of the plates, plus that of the piece and carriage, over 
the path S, will be equal to the total .energy of recoil. 

/(P + nP )xS = ^f (352), 


In this equation, for a given value of 5, everything is 
known except P„ and its value can be determined so as to 
limit the recoil to a given length S. 

Objections. — The objections to friction-brakes are : 
i. They oppose to the initial motion of the system, the 
maximum resistance, when the velocity of recoil is greatest, 
and hence the resistance is not uniform during the recoil. 

2. The resistance is not constant for any two consecutive 
shots, since it varies with the condition of the surfaces in 
contact. For the first shot, if the surfaces are slightly rusty, 
the resistance will be great; for succeeding shots, as the 
surfaces become polished, the resistance decreases, and if 
the surfaces be wet or lubricated, the resistance decreases. 
All these causes necessitate a regulation of the pressure for 
each shot. 

3. The friction-brake is not automatic, as it has to be 
undamped after each shot, to allow the gun to run in battery, 
and has then to be clamped again before firing. Accidents 
are liable to occur from this cause. 

For these reasons the friction-brake has been abandoned 
for seacoast guns, and is only retained in different forms in 
field guns, where the weight of the hydraulic buffer, and its 
liability to get out of order, would be objectionable. 

261. Hydraulic Brakes — General Description — Classification — Object 
of Discussion. 

General Description. — This brake consists of one or 
more cylinders filled with non-freezing liquid, and attached 
either to the chassis, or to the top carriage. In modern 
carriages the cylinders are generally two in number, and 
are attached to the top carriage as near the axis of the gun 
as possible, to increase the mass of the system recoiling, and 
thus diminish its velocity; and also to bring the line of re- 
sistance of the brakes as nearly as possible coincident with 
the axis of the bore, and thus diminish the overturning 

In each cylinder moves a piston, pierced with holes 
parallel to the axis of the cylinder, and having a piston-rod 
attached to the chassis. 


When the piece and top carriage recoil, the cylinders 
move to the rear, and the liquid is forced through the holes 
in the pistons. The resistance which the liquid opposes to 
the motion of the pistons, limits the recoil. 

Classification. — There are two kinds of hydraulic 
brakes in use : 

i. Those with constant orifices and variable resistance. 

2. Those with variable orifices and constant resistance. 

Object of Discussion. — The principal points to be de- 
termined in discussing a hydraulic brake are : 

i . The length of recoil ; 

2. The area of orifice ; 

3. The pressure in the hydraulic cylinder; 

4. For the hydraulic brake of constant resistance, the 
law of variation of the areas of orifice, in order that the re- 
sistance shall be constant. 

In the discussion, the friction of the liquid is neglected, 
as this is found in practice to be small. The flow, also, is 
supposed to take place through a thin partition, so that the 
contraction of the liquid vein may be neglected. 

The velocity at the beginning of motion, is supposed to 

be the maximum velocity of recoil. 


262. Hydraulic Brakes with Constant Orifice and Variable Resist-, 
ance — Nomenclature — Value of Total Resistance Opposing 

Nomenclature. — Let A be the effective area of cross- 
section of the piston ; that is, the area of the piston minus 
that of the piston-rod and orifices ; 

a, the area of the orifices of flow ; 
*V m ', the maximum velocity of recoil of the system ; 
v' , the velocity of recoil at any time t ; 
v, the velocity of flow of the liquid through the 

orifices at that time : 
P, the weight of the system recoiling; 
a, the angle of inclination of the chassis to the 

horizontal ; ^ 

S, the density of the liquid filling the cylinder 
(weight of unit volume) : 

* With the brake acting. 


/, the coefficient of friction ; 
F, the total resistance which opposes the recoil. 
Value of F. — The total resistance, F, is composed of 
two parts : 

i. The resistance of the brake, F'. 

2. The resistance due to the friction of the moving parts, 
and the inclination of the chassis, F". 
We have then 

F=F' + F" (353) 

The value of F" is 

F" — P{sina-\-/cosa) (354) 

The value of F', the resistance of the brake, is equal to 
the total pressure exerted by the piston upon the liquid. 

To determine this, we know from the law of continuity 
of the fluid, that the volume of liquid displaced by the pis- 
ton, must be equal to that which passes through the orifices 
in it ; hence we have 

v'A = va, (355) 


v = -^~- (356) 

This velocity v is that due to a height of fall 

v= V2gH; (357) 

and if we suppose a column of liquid whose constant height 
is H and density 8, it will produce a pressure per unit of 
surface at its base, sufficient to cause the velocity of flow v. 
Hence this is the pressure exerted per unit of surface by 
the piston, upon the liquid, or it is the weight of a column 
of liquid whose height is H, density 8, and area of base 
unity. This pressure is 

P = 8XH, (358) 

and the total pressure on the surface A of the piston is 

pA=F' = 8xHxA, (359) 



H =^A (36o) 

Substituting for v and H in (357) their values from (356) 
and (360), we have 

from which 

a ~ r 8 A 

F' = — (361) 

2gd i VJ ' 

Substituting the values of F' and F" from (361) and (354) 
in (353), we have for the value of the total resistance to 

SAW 2 
F= ~^tf~ + P ( sma +f cosa )- • • • (3 62 ) 

263. Length of Recoil with Constant Orifice. 

Dividing both members of equation (362) by M, we have 
for the acceleration of recoil 

i = W = - [Mr *" + * (sin a + / cos ">]• ^63) 


Zi — ti 


we have 




g(s\w a +/cos a) = K, 


-(Bv»+K). (364) 

dx — v'dt, .: dt = — T , 

dv' v'di/ 

-*=-*r = -w+z). • • (36s) 



d *=-LW^TK &*> 

Integrating between the limits VJ and v', 

C Vm ' v'dv' i , (BV m n + K\ .,, 

,/, - Bv" + AT = * = ^bg~e lQ S (^ 2fe» + K ) ■ (367) 

Replacing B and ^T by their values, we obtain an 
equation giving the relation between v' and x which is too 
complex for general use. To simplify it, make 

f=o, a = o,_ 

which is equivalent to supposing that the brake acts alone, 
without friction, and that the chassis is horizontal. 
In this case we have 

K= o; 
and substituting this value of K in (367), we have 

2Pa' , V m ' 

* = ^4Mo:g-7 lo s^r (368) 

When v' = o, at the end of recoil, x = 00 from equation 
(368), which shows that the recoil will continue indefinitely 
if the brake with constant orifices act without the aid of 

264. Area of Orifice for a Given Length of Recoil with Constant 
Orifices — Pressure in Cylinder. 

Since for v' = o, x = 00, we cannot find directly from 
equation (368) the area of orifice which will limit the recoil 
to a fixed length /. This area can, however, for all prac- 
tical purposes be determined as follows : 

Suppose that when 

v' = v,' 

the remaining energy of the system becomes very small, and 
the carriage is about to come to rest, and let / denote the 
length of recoil for which v' = v v '. Then, from (368), 


8A z l\oee 

** = T5w (369) 

2P log ~^r 

for the area which will give the length of recoil /. 

Pressure in Cylinder. — The total pressure in the 
cylinder at the beginning of recoil is, from (361), 


2ga' ■ 
and at any time at which velocity is v' it is 

F' = — (371) 

2ga' ' vo/ ' 

and the pressure per unit of area will be 
F' 8 A" VJ 


A ~ 2gC? 

F; 8A"v n 
A " 2gd 



265. Hydraulic Brake with Variable Orifices and Constant Resist- 
ance — Reason for Using it — Objects of Discussion — Value of 
Total Resistance opposing Recoil. 

Reason for using Brake with Constant Resist- 
ance. — For the brake with variable resistance, equations 
(372) show that the resistance is greatest when the velocity 
of recoil is greatest. This is contrary to the first condition 
imposed upon a good brake, and it evidently throws a great 
strain upon the carriage. 

For this reason these brakes are no longer used with 
modern carriages, but are replaced by those whose orifice of 
flow is large at first, so as to allow a free flow of liquid 
when the velocity of recoil is greatest. As the velocity of 
recoil decreases, and its length increases, the orifices of flow 
are gradually closed automatically, and the resistance thus 
made constant throughout the recoil. 


Objects of Discussion. — The objects of the discussion 
are to determine — 

1. The length of recoil ; 

2. The maximum area of the orifice of flow ; 

3. The law of variation of the area of orifice in order 
that the resistance shall be constant; 

4. The constant pressure in the cylinder. 

In this discussion, the first period of recoil, during which 
the resistance is approaching its constant value, is neglected, 
as being very short, and the resistance is supposed to be 
constant from the beginning of recoil. 

Total Resistance opposing Recoil. — The nomen- 
clature being the same as before, let a t be the maximum 
area of orifice of flow, and suppose it to be also the initial 

Then we have, as in the case of the brake with constant 
orifice, equation (354), 

F" = /'(sin a -(-/cos a) (373) 

Also, equation (361), 

F ' = -&- ( 374 > 

Since F' is constant by hypothesis, we must have for any 
other values of v' and a, as VJ and a a , 

_, 6A*V m n . . 

F =^T' (375) 

from which 

ft A 3 V " 
F=F' +F" = f- + P(sm « + / cos a). (376) 

266. Length of Recoil with Variable Orifice. 

Dividing both members of equation (376) by M, we have 
for the acceleration of recoil, as before (equation 363), 

dv' F_ 
~~di ~~M 

2 p a . + £"( sin « + / cos a) 


at ^ <-■ *»o t 



V = - [_^f +^(sin a -f /cos a)\t + C. (378) 
When t = o, v' — V m ' — C, hence 

°-^- +^(sin a +/COS a)\t. (379) 
Integrating again, 

* = *V'-jP^V+#(sin«+/cos «)]/», . (380) 
which is of the same form as 

>* = vt - \gf, 

and hence it is the equation of a uniformly retarded motion, 
as it should be, since the resistance is constant. 

When the recoil ceases v' = o, and x = /, the total 
length of recoil, and the corresponding time is, from (379), 

T = **V> * J ^ := • • (380 

2 p % + ^"(sm a. + / cos a) 

and this value of *T in (380) gives for the total length of 

1 n v n n ~ 1 

I -^3-+<f(sina+/cos«)j, 

Equations (381) and (382) are similar to 
v v 1 

for bodies falling freely in vacuo, under the action of gravity, 
as should be the case, since we have a constant force acting 
in both cases. 

Placing equation (382) in the form 


8A* 2g-(sin a -\- f cos a) ' 


we see that / increases as VJ increases and as a decreases, 
which should be the case. 

267. Maximum Area of Orifice for the Brake with Variable Orifices. 

To find the value of #„, the maximum area of orifice in 
this case, solve equation (382) for a*, and we have 

. $IA* 1 

2gl (sin a -{-/"cos a) 
1 y~^ 

v m 


for the maximum area of orifice. 

Suppose the chassis horizontal and the top carriage 
mounted on rollers so as to avoid friction ; then 

« = o, / = o, 
and (384) becomes 

<-<£ (385) 

The area of orifice in this case is independent of the 
velocity of recoil, and hence we conclude that if the top 
carriage be placed on rollers and the chassis be horizontal, 
the length of recoil will be the same for a given area of 
orifice, no matter what the initial velocity of the projectile, 
charge of powder, or angle of fire may be. 

268. Law of Variation of Areas of Orifice for Constant Pressure in 

The energy of the system at the beginning of recoil is 

PV " 
— ; after passing over the length of recoil x, when the 

velocity is v', the energy is , and the work done over 

the path x is Rx, in which 


at g at 

From mechanics, the original energy of the system is 
equal to its remaining energy after passing over a given 
path, plus the work done over that path ; hence 

PV m n Pv" P dv> 

= x—rr, .... (386) 


* = VJy/ i _ 

2X ~T~ 
-f~ (387) 

V in 

Since the resistance is constant and the recoil uniformly 
retarded, we have from the laws of constant forces 

V m " = 2gk = 2^l. (388) 

Substituting this value of VJ* under the radical sign in 
(387), we have 

v'= V m \/ T --, (389) 

Since F' is constant, we have, from (374) and (375), 


2gd i 2ga 
v' a 

VJ a! 



Dividing through by VJ in (389) and substituting for 

-jjrj its value from (391), we have 

a = a \/ l — 7 ! (39 2 ) 1 

that is, the areas vary as the ordinates of a parabola. 


These variable areas of orifice are obtained in different 
ways, one of the methods adopted in our service being to 
cut rectangular notches in the piston-head, and have bars 
bolted to the sides of the hydraulic cylinders, parallel to the 
axis, whose profile is such that at the origin the maximum 
opening will be a . 

269. Profile of Rib for Constant Pressure — Maximum Pressure in 

The profile of the rib or throttling-bar will then be a 
parabola. As the piston moves down the cylinder, the 
areas of orifice will be gradually diminished so that the 
pressure shall remain constant. 

The equation of the parabola giving the profile of the 
rib is determined as follows : 

Suppose there are n similar notches in the piston-head. 

The area of each one will be — . Let b and d be the breadth 


and depth of each notch. The rib in the cylinder must 
have the same breadth, b, and a variable depth, y. 

Then for the area of an orifice at any time we have 

- = b(d-y), .\a — nb(d—y), . . . (393) 

and this value of a in (392) gives 

'-'- v^i • • • 


for the equation of the curve of the profile of the rib. 

Pressure in Cylinder. — This is given by equation 


p ,_ osij^__ c _ aconstant # _ / 39S ) 


and per unit of area 

F' 8A'V m 

A 2ga: 

C = a constant. . . (396) 



270. Definitions. 

Pointing. — To point a piece is to give it such a direction 
and elevation that the projectile, when fired, will hit the 
object aimed at. 

Operations. — The pointing of a piece includes two dis- 
tinct operations : 

i. Giving the axis of the gun an elevation such that the 
projectile shall strike at the proper distance, or range, from 
the muzzle. 

2. Giving the axis of the gun such a direction that the 
projectile shall strike a given point or object at that distance. 

Sights. — The instruments used in pointing are called 
sights, and there are two of these for each piece : the front 
sight and the rear sight. 

Front Sight. — This is fixed to the muzzle of the gun, or 
to one of the rimbases, usually the right, and consists gen- 
erally of a fixed point, or thin edge, or of cross-wires in a 
tube, the point, edge, or cross-wires being at a definite dis- 
tance above the axis of the bore, and if on the rimbase, at a 
fixed distance to the right or left of that axis. 

Rear Sight. — This generally consists of a rod, bar, or 
standard, graduated in degrees or ranges, and fixed in a 
socket on the breech of the gun. This standard carries a 
sliding notch or small hole, which is capable of being ad- 
justed to any height on the rod, corresponding to a given 
range or elevation, within service limits. The notch or hole 
has also a motion at right angles to the axis of the bore, to 
correct for wind, drift, and other causes of lateral deflection. 




In Fig. 262 let A represent the front sight ; 
OC, the rear-sight standard ; 
EC, the sliding piece, which is supposed to 
be at right angles to OC; 
E, the rear-sight notch. 
Triangle of Sight. — Then the triangle OCE is called the 
triangle of sight, and ECO is a right angle. 

Zero of the Rear Sight. — The point O, where the line OA, 
drawn parallel to the axis of the piece through the top of 
the front sight, intersects the axis of the rear sight. 

Natural Line of Sight. — The line OAB, parallel to the 
axis of the piece, and passing through the zero of the rear 
sight and the top of the front sight. 

Sight Radius. — The length of the line OA. 

Artificial Line of Sight. — Any line, such as EAF, passing 
through the notch of the rear sight and the top of the front 

Natural and Artificial Planes of Sight. — The vertical 
planes containing the natural and artificial lines of sight 

Plane of the Rear Sight. — The plane perpendicular to the 
axis of the piece, containing the triangle ECO. 

271. Cases which may occur in Pointing — First Case — Height of 
Rear Sight — Corrections for Drift. 

Cases. — The following cases may occur in pointing: 
1. The axis of the trunnions may be horizontal, and the 

target situated in the horizontal plane passing through the 

centre of the muzzle. 



2. The axis of the trunnions may be horizontal, and the 
target situated above or below the horizontal plane through 
the muzzle. 

3. The axis of the trunnions may be inclined, and the 
target situated in the horizontal plane. 

4. The axis of the trunnions may be inclined, and the 
target situated above or below the horizontal plane." 

The second case is the usual one for sea-coast guns, and 
the fourth for field guns. 

First Case. — In Fig. 263 let 
HB represent the line of fire projected on the vertical 

plane ; 
H'B', the same line projected on the horizontal plane ; 
D and D' , the target ; 

CAD and F'A'D', the projections of the artificial line of 
sight on the vertical and horizontal planes respect- 
Then CO is the height of the rear sight necessary to hit 
the point D, and F'C the correction for drift 

Fig. 263. 

If these distances be known for a given range MD, it is 
evident that by fixing the rear sight with the proper eleva- 
tion and drift, and giving the axis of the gun the direction 
shown, the target will be struck. 

To Calculate Height of Rear Sight. — In Fig. 263 
let h be the height of the rear sight CO ; 


/, the length of the sight radius OA ; 
0, the angle of elevation BMD, the line MD being hori- 
zontal ; 
6, the angle CA made by the natural and artificial 

lines of sight ; 
d, the angle MDG. 
Then in the triangle MDG we have 


But the angle MGD = CAO = 6, hence 

6 = - 8. 

The angle (J is always very small, being the angle sub- 
tended at the target by the vertical projection of the chase 
of the gun from front sight to muzzle, and hence we have 




tan 6 = tan ; 

/> h 
tan a = j ; 

.=tan0; .-. k = / tan (p. . . . (397) 

This value of h is laid off on the rear sight from the zero, 
and gives the graduation corresponding to the angle 0. 
Correction for Drift. — In Fig. 263 let 
D denote the drift B'D'\ 

d, the distance F'C, or the correction for drift; 
rj), the angle of drift, B'M'D'. 
In the similar triangles F'A'C' and N'A'D' we have 

F'C' _N'D\ . F , r ,_ d _ r , A ,N'n , . 

CA'-WN" ■■ FC - d ~ CA A r N>- ■ (398) 



C'A' = CA, nearly, = ^ A/ ^ = zr; 

^ cos C^4 C cos 6/ 

or, since -- <f>, 

C' A ' = — ^i- 




The distance N'D' is very nearly equal to the drift B'D ', 
and A'N' — M'B', or the range R, very nearly. 
Making these substitutions in (398), we have 


d =R^6T4> (399) 

272. Second Case. 

In this case the axis of the trunnions is horizontal, and 
the target above or below the horizontal plane through the 

In Fig. 264 let D be the target situated above the hori- 
zontal plane MD' 1 ; 
<p, the angle BMD; 

a, the angle of elevation of the target 
above the horizontal plane. 

Fig. 264. 

In the deduction of the equations of Exterior Ballistics, 
the horizontal plane MD" through the centre of the muzzle, 
is alone considered, and all functions of the trajectory re- 
ferred to this plane. 

By the principle of the rigidit) r of the trajectory, the 
curve may be revolved through a certain angle about a hori- 
zontal axis passing through the point M, without changing 
the relations between the curve, its ordinates and angles, 
and the chord MD". 

For all practical purposes the points M and A may be 
considered as coinciding, and the revolution as taking place 
about the latter point. 

Hence if the proper elevation OC, and correction for 
drift, be obtained from equations (397) and (399) for the range 
MD" = MD, on the supposition that the target is situated 
on the horizontal plane, and then the gun be revolved about 
the axis of the trunnions through the angle a, till the line 



of sight CA passes through the point D, the projectile will 
hit the target, since this is equivalent to revolving the 
whole trajectory for the given range MD" through the angle 
a. The same discussion applies to the drift, which is not 
altered by the elevation of the target, but is the same for 
the same range. 

Hence, for this case, give the rear sight the same eleva- 
tion and correction for drift as if the target were situated 
on the horizontal plane through the muzzle, and then ele- 
vate the gun till the artificial line of sight passes through 
the target. 

273. Third Case— Errors — Fourth Case. 

Third Case. — In this case the axis of the trunnions is 
inclined, and the target is in the horizontal plane through 
centre of muzzle. 

Let Fig. 265 be a section of the gun through the plane 
of the rear sight, the axis of the bore being horizontal. The 
zero of the rear sight, and top 
of front sight, are projected 
at O. 

Let OC be the correct ele- 
vation, and FC the correction 
for drift, which will cause the 
projectile to strike the target. 

Suppose that, due to inequal- 
ities of the ground or other 
causes, the gun is rotated to the 
right, about the axis of the bore, 
through the angle 8. The zero 
of the rear sight, and top of 
front sight, will now be pro- 
jected at O', and the new posi- 
tion of the rear sight will be 
O'C'F'. The axis of the bore 
or line of fire has not changed 
its position, and the gun, if 
fired, will hit the target. But 
if the gun be resighted before 
firing, using the sights in their Fig. 265. 


revolved position, the artificial line of sight will no longer 
pass through the target, and if it be made to do so, this will 
change the position of the line of fire, or axis of bore; and 
the projectile will no longer strike the target. 

Errors. — By this rotation of the gun, the following 
errors have been introduced : 

i. Instead of having the proper vertical height of rear 
sight equal to OC or 0"C", it is equal to 0"C", or too 

This may be explained as follows : The front sight, and 
zero of rear sight projected at O, have been lowered verti- 
cally by the rotation a distance 0"0 ; and since the height of 
rear sight above the zero should remain unchanged, this 
height should now be 0"C", equal to OC. But the rear- 
sight notch is actually at a height 0"C", and hence is too 
low by the distance C"C". 

2. Instead of having the proper correction for drift FC, 
we have F iv C, which is too small. 

3. The artificial line of sight, before rotation occurs, 
passes through the point F, and the top of the front sight 
projected at O. Hence, looking from the rear, the line of 
sight FO is oblique to the axis of the gun and diverges to 
the right. 

After rotation the artificial line of sight passes through 
F', and the top of the front sight projected at O'. Hence, 
looking from the rear, this new line of sight F'O' is oblique 
to the axis of the gun and diverges to the left. If, therefore 
the gun were correctly pointed before rotation, and be re- 
pointed after rotation, the projectile will deviate to the 

This latter error is shown in plan, the same letters being 
used. It is of very frequent occurrence in small-arms firing, 
when the rear sight is not held vertically, the bullet deviat- 
ing to the side toward which the sight is inclined. 

To avoid these errors it is necessary to construct the 
rear sight so that its standard or upright will rotate about 
the point O. By means of a spirit-level fixed at right angles 
to the axis OC, this axis can always be kept in a vertical 
plane. With this arrangement, whenever the front sight 



and the zero of the rear sight are lowered vertically through 
a distance 0"0, by rotation due to the inequality of the 
ground or other causes, the notch of the rear sight will be 
lowered the same amount, the vertical heights (9Cand O'C" 
and the correction for drift remaining unchanged. This 
arrangement is made in all field-gun sights. 

With this arrangement of the sights the pieces are pointed 
as in the first case. 

Fourth Case. — In this case the axis of the trunnions 
is inclined, and the target above or below the horizontal 

If the standard of the rear sight rotates about the zero, 
as explained, the pointing is executed as in case two. 

O 7* 

Fig. 266. 

274. Permanent Angle of Drift. 

Referring to Fig. 263, it is evident that the drift increases 
more rapidly than the range, and hence each range requires 
a special correction for drift. It is found, however, that 
within certain limits of error, a permanent correction may 
be made for drift, by giving the rear-sight standard an in- 
clination to the left at a certain angle i with the vertical. 
This applies only to small arms where the barrel can be 
held with the front sight vertical, and to guns with fixed 
platforms, where the axes of the trunnions are horizontal. 
For field-guns, as before explained, the standard of the rear 
sight is kept vertical. 

To determine this permanent angle, in Fig. 266 

let i = the angle FOC required ; 
h — OC, the height of rear sight ; 
d = FC, the correction for drift , 
/= OA, the length of the sight radius; 


<p — the angle of elevation BAD ; 
e = the angle DAD'. 

Then in the triangle FOC we have 

d — h tan i ; 

but from (397), 


h = /tan ; 

d = / tan tan z, 

tan 1 =7— — - (400) 

/ tan (ft vt / 

From the triangle OAC we have 

AC = I sec (f>, (40 1 ) 

and from FAC, 

or from (401), 

but from the figure, 

hence in (401a) 

d = AC tan e, 

d — I sec <p tan £ ; . . . . (401a) 
DH drift 

tan e = 

AD range' 

d = I sec <pj: (402) 

D denoting the drift and R the range. 

Substituting this value of d in (400), we have 


tan z = p . , (40s) 

R sin 4> 

It is known from Exterior Ballistics that sin <f> increases 
more rapidly than the range, and so also does D. Hence 
these variations partly correct each other and tend to make 
the angle z constant, and hence this constant correction for 
drift can be applied without great error. For long ranges, 
however, this correction is only partial, and an additional 
one must be made with the sight. 


From equation (403) the amount of drift corrected for by 
this method is 

D = R sin <f> tan i ; 

if any greater drift exists, as D' ', the difference, 

D' — D = D' — R sin <p tan i, 

must be corrected for by the sight. 

275. Indirect Pointing. 

When the target cannot be seen from the gun, the above 
methods must be modified. 

The simplest case is that of mortar-firing, where the tar- 
get is invisible from the piece, but may be seen from the 
parapet of the emplacement. In this case the plane of sight 
is established by plummets suspended from trestles, the ele- 
vation given approximately, and the mortar moved or trav- 
ersed, till the planes of fire and of sight coincide. 

The second case is where the target cannot be seen from 
the battery, but is visible from some place sufficiently near 
to communicate with the battery. In this case an observer 
watches the point of fall, and signals to the battery its posi- 
tion as to range and deviation. The aim is then corrected, 
and this is continued till the target is struck. An auxiliary 
mark, which is visible from the gun, is selected, and the sights 
directed upon this mark before each shot. When the target 
is struck, the piece is thereafter sighted upon this auxiliary 
mark, without changing the sights as adjusted for that shot. 
If a suitable mark cannot be obtained, the bearing of the 
target may be observed by a compass. Then by placing 
the compass in rear of the gun, the bearing of the target may 
be laid off by stakes and the gun directed upon them, the 
firing being corrected by an observer. 

In some services sights are arranged so that they may- 
be reversed in position ; that is. the rear sight is placed in 
the position ordinarily occupied bv the front sight, and the 
latter replaces the rear sight. (See 7-inch howitzer sight, 
page 493.) In this case the marking stake or stakes are 
placed in rear, and the sights directed upon them. Reflect- 
ing sights are also used when cover is of importance, and 


for turrets, the sights are placed on the exterior, and at the 
opposite extremity of the diameter upon which the gun is 
situated. While the turret is revolved 180 for loading, the 
sighting is effected, and when the gun is loaded, a traverse 
of 180 brings the gun into firing position. 

276. Causes of Deviations in Pointing — Effect of Wind. 

Causes of Deviations. — When a gun is correctly 
pointed, as explained, the projectile should pass through 
the target. This, however, does not occur unless further 
corrections be made to eliminate other causes of error. 

The principal of these are : 

i. The effect of the wind. 

2. Errors in estimating distance to target. 

3. Effects of light on sights. 

4. Personal errors of the eye. 

5. Errors in height of front and rear sights. 

6. Motion of target. 

7. Rotation of the earth. 

8. Variations in ammunition. 

9. Jump. 

Effect of Wind. — The effect of wind is to increase or 
decrease the range, according as it is blowing from rear to 
front, or from front to rear, and to increase or decrease the 
drift of the projectile. 

The velocity of the wind is generally expressed in miles 
per hour, and is obtained from an anemometer. A vane or 
other indicator gives its direction. Let W be the velocity 
of the wind in miles per hour, and <f> the angle which its 
direction makes with the line of fire. The angle cf> is meas- 
ured from front to rear, being zero when the wind blows 
directly from the front along the line of fire. 

Then the component which increases or decreases the 
range is W cos 0, and that which increases or decreases 
the drift is J^sin <p. 

The effect upon the increase or decrease of range is ob- 
tained by reducing W to feet, and regarding the projectile 
as having a velocity equal to v -\- W cos <p or v — W cos <p. 


Using these values for v in the ballistic formulas, the effect 
of the wind along the range can be calculated. 

The component which produces deviation is W sin <p. 
Various formulas are given for calculating its effect, but the 
subject is very difficult. 

When the wind is blowing from the left, its relative mo- 
tion with respect to the projectile is less because the latter 
is moving in the same direction. When it blows from the 
opposite direction the reverse is the case. To correct for 
lateral deviation due to wind, the drift-slide is set towards 
the wind. That is, if the wind is from the left, the slide is 
moved to the left. 

For small-arm firing, the direction of the wind is ex- 
pressed by a clock-face notation, the clock being supposed 
to be held in the hand of the firer, with the Xll-o'clock 
mark toward the target and the Ill-o'clock mark to the 
right. A wind blowing directly from the target is called a 
Xll-o'clock wind ; one directly from the left, a IX-o'clock 
wind, etc. 

Assuming the force of the wind as unity, a table is given 
in the " Rifle and Carbine Firing," showing the proportions 
of the rectangular components of the different winds, and it 
is found practically, that the lateral deflections produced by 
them are proportional to these components. 

The amount of lateral deviation produced by a wind 
blowing at right angles to the line of fire, with a velocity of 
one mile per hour, is called the coefficient of deviation. 
Calling this coefficient k, we have for any wind whose 
velocity is W, and which makes an angle q> with the line of 
fire, for any given range, 

D — kWsxxi 0. 

The relation between k and R must be determined by 

277. Estimating Distances — By the Eye— By Sound — Le Boulenge 

It is evident that unless the distance of the target be 
known, the proper elevation and correction for drift cannot 


be given, since these depend on the range. In actual opera- 
tions the distance of the target is seldom known. For sea- 
coast guns, the channel or harbor is surveyed and plotted, 
and buoys may be planted at different known distances. In 
siege operations, the distance of the target may be obtained 
by observations with various instruments of precision ; but 
for field artillery, where time is lacking, the distance must 
be obtained rapidly by estimation, by range-finders, or by 
trial shots. 

Distances may be estimated — 
i. By the eye ; 
2. By sound. 

By the Eye.— This method requires considerable prac- 
tice to obtain results of any accuracy. For short ranges 
the eye may be trained by trial, by observing carefully 
the appearance presented by known objects at different dis- 
tances, such as the height of a man, the parts of his dress, 
etc., which are visible at those distances. Each individual 
must form a standard of comparison for himself ; and since 
this method is only applicable for relatively short distances, 
it is of more importance for small-arm fire. 

Objects vary in appearance according to the nature of 
the ground, being apparently nearer for level ground ; also 
on a clear day, or with a distinct background, they appear 
nearer than under opposite conditions. 

By Sound. — This method is based on the fact that 
sound travels about uoo feet per second in air. Hence, if 
the time in seconds be noted between the flash and the re- 
port of a gun, or between the flash and the report of a shell 
fired from the battery, the distance is obtained by multiply- 
ing the time in seconds by noo feet. This time may be 
measured by a stop-watch, or by counting the number of 
steps taken in the interval, and knowing the number of 
similar steps which the observer takes per second. 

Le Boulenge Telemeter. — An instrument called the 
Le Bouleng6 telemeter is used for measuring distances' by 
sound. It consists of a glass tube filled with liquid,^ in 
which a disk is placed, whose specific gravity is slightly 
greater than that of the liquid. When the tube is held ver- 



tical, the disk falls through the liquid with a motion which 
is nearly uniform. To use the telemeter, the tube is held 
horizontal, with the disk at zero. When the flash is seen, it 
is turned quickly to a vertical position ; when the report is 
heard, it is turned back to a horizontal position. A scale on 
the tube gives the range directly, corresponding to the dis- 
tance passed over by the disk. 

It is evident that it would be difficult in practice to 
observe the burst, and hear the report of any particular 

278. Range-Finders — Principle — Class 1. 

The estimation of distances by the eye and by sound 
being so inaccurate, instruments called range-finders or 
telemeters have been devised to measure the distance to the 


Fig. 267. 

Principle.— In Fig. 267 let C be the target. 

In the isosceles triangle ADC, if the angles at A and D, 
and the base AD, are known, the angle ACD can be found, 
and we have 

\AD . 


tan i A CD' 

or in the right-angled triangle ABC or BCD, if the angle 
at A or D be known, we have 

BC = 

tan ACB' 




AC = 


sin A CB' 

The object of these instruments is to measure rapidly 
and accurately the angles A and D. 

To avoid calculations, the angles A and D are so chosen 
that the value of the tangent or sine of C shall be some sim- 
ple number, as fa, fa, fa, etc. ; or the angles may vary and 
the base have a fixed value, the corresponding multipliers 
being inscribed on the instrument. 

This divides the instruments into two general classes — 

i. Those having fixed angles and variable bases ; 

2. Those having variable angles and fixed bases 

Fig. 268. 

and a third class which combines the qualities of the two 
above, viz., 

3. Those having variable angles and variable bases. 

Class i. — In this class of range-finders the base is pro- 
portional to the range. This gives greater accuracy, as 
with a small base, a slight error in measurement of either 
angles or base leads to a large error in range. The general 
idea of this class of instruments is as follows : Two mirrors 
are fixed at an angle, say, of 44° 17' (Fig. 268). A ray of 
light striking one of these mirrors is reflected twice, and 
according to a well-known principle of optics, the ray, after 
two reflections, makes with the original direction of the inci- 


dent ray, an angle of 88° 34', or twice the angle of the 
mirrors. An observer standing at A and looking toward i>» 
sees B directly, and by reflection in the mirrors, makes the 
image of C coincide with B. The point A is then marked 
by a stake. Moving to B, which must be found by moving 
along AB and looking towards A, the reflection of C is 
made to coincide with A. The angle at C \s then 

i8o°-2 X 88° 34' = 2 52', 

and measuring AB we have 

AC= _*^?_ = *d£ 
sin i° 26' ' ^ ' 

AC = 40 X \AB - 20AB. 

Fig. 269. 

279. Range-finders — Glass 2 — Glass 3 — Depression Range-finders 
— Range and Position Finder. 

Class 2. — In this class we have a fixed base and a variable 
angle. To save time, the instruments are generally adjusted 
so that the range can be read off at once. As the measure- 
ments must be very accurate, telescopes are often used to 
measure the angles, and this necessitates a very accurate 
mounting and increases the difficulty of transportation. 

Class 3. — These instruments can be used by either 
method, but the variable base is generally preferred. 

Depression Range-finders. — Let AB, Fig. 269, repre- 
sent the vertical height of a gun, or of a range-finder, above 
the surface of the water, and C an object, such as a ship, 
whose distance is to be determined. If the angle C'BC be 
measured, and the height AB be known, it is evident that 
the distance BC can be determined as before. These instru- 



ments are called depression range-finders* the angle being 
measured in a vertical plane. 

Range and Position Finders. — In sea-coast batteries 
it is often necessary to fire at objects, such as ships, which 
cannot be seen from the guns. In this case it is necessary 
to find not only the range but. also the position of the object, 
which is generally in motion, in order to hit it at any given 
time. An instrument used for this purpose' is the Fiske 
Range and Position Finder, invented by Lieut. Fiske of the 
U. S. Navy. 

Fig. 270. 

Fig. 271. 

280. The Fiske Range-finder. 

In Fig. 270 let A represent the target, and BC a known 
base. Then 

AC: BC:: sin ABC : sin BAC. 


sin AB C 
sin BAC 

The angle ABC can be readily measured. The angle 
BAC= DBE, the line BE being parallel to AC. The Fiske 
Range-finder rrieasures the angle DBE by the use of the 
Wheatstone bridge, as follows : 

Suppose the two semicircles in Fig. 270 replaced by two 
metallic arcs (Fig. 271). At the centre of each of these arcs 


is pivoted a telescope, the pivot of which is connected to a 
battery, B. The telescopes are in electrical contact with 
the arcs. These metallic arcs are connected at their ex- 
tremities with a galvanometer, c, the whole forming a 
Wheatstone bridge, whose arms are aabb. 

When the two telescopes are pointed on the object A, 
it is evident that the arms of the bridge are unequal, and 
hence do not balance, and this fact is indicated by the de- 
flection of the needle of the galvanometer. The arc FD is 

By swinging the telescope at F, around, till the needle of 
the galvanometer indicates zero, the bridge balances, the tele- 
scope being parallel to the one at C, and the arc or angle 
DF — FE — DE is equal to the angle at A. From this the 
distance AC can be calculated, or be read off directly on a 
properly constructed scale. 

Generally, in using the instrument, the telescopes are 
mounted at a distance from the battery where the view is 
uninterrupted, while the galvanometer is at the gun. The 
observers keep the telescopes constantly directed on the 
target, and the man at the gun balances the bridge, by intro- 
ducing a variable resistance into the circuit, till the needle 
stands at zero. This variable resistance is graduated so as 
to indicate the range corresponding to the resistance in- 

281. The Fiske Position-finder— Range by Trial Shots. 

To find the position of the object, the Fiske Range- 
finder is modified as follows, Fig. 272. 

Let A and B be the arcs with their telescopes as de- 
scribed, and'D a chart drawn to scale, on which are two 
metallic arcs, A' and B' . The arc A 1 is connected electri- 
cally with A and with a galvanometer, A", forming a 
Wheatstone bridge, and in the same way the arc B' is con- 
nected with B, and with the galvanometer, B" . The arc A' 
carries a metallic rule, A'C, pivoted at the centre of the arc, 
and B' a rule, B'C, similarly pivoted. 

When the rule A'^C is parallel to the telescope at A, the 
galvanometer A" is at zero. When B'C is parallel to the 



telescope at B, the galvanometer B" is at zero. Hence their 
intersection C marks the position of the object on the chart. 
Let G be the gun in battery, and G' its corresponding posi- 
tion on the chart. The gun has a metallic arc with which a 
pointer is in contact, and the arc G' has a metallic rule, G'C, 
in contact with it. The gun G with its arc and pointer, and 
the metallic rule G'C', are electrically connected with a gal- 
vanometer, G", near the gun, forming a third Wheatstone 
bridge. It is evident that by traversing the gun in azimuth 
till its axis is parallel to the rule G'C, the galvanometer G' r 

A"'' S" 

Fig. 272. 

will indicate zero, and the gun will have the proper direc- 
tion. The elevation may be telephoned from the observing 
station, or else the gunner, knowing the range and direction 
of the object, may take the elevation directly from a range 
table. Other arrangements of the same nature may be 
made with this instrument, using the principle of the 
Wheatstone bridge. 

Range by Trial Shots. — Owing to various causes, 


the determination of distances in the field by range- 
finders is attended with difficulty, and the method actually 
adopted in all services is that by trial shots. Two plans are 

In the first a percussion-shell is fired with an elevation 
which will cause it to strike short of the target. The point 
of fall is observed. A second shell is then fired with an 
elevation which will cause it to strike beyond the target. 
Its point of fall is also observed. The target is then en- 
closed in a fork. 

Taking a mean of these two elevations will give a still 
closer approximation. If this shot' falls short, a mean of 
this elevation and of that beyond will give another approx- 
imation, and so on. 

By this means the range is soon found. 

The second method is to fire the first shot short, and 
then increase the elevation slightly, and so on by succes- 
sive increments till the proper range is attained. The diffi- 
culty is in observing accurately the point of fall for long 

282. Effect of Light— Errors of the Eye — Errors in Height of Front 
and Rear Sights. 

Errors due to Light. — In clear weather shots usually 
fall short, since, in a bright light, objects appear nearer, and 
the distance is underestimated, and, in addition, a finer sight 
is taken, owing to the distinctness of the front sight. The 
converse is true on a dark day. With regard to lateral 
deviation, if one side of the sight is brighter than the other 
the deviation will be from the light. 

Errors of the Eye. — These vary with different indi- 
viduals, and must be corrected by training. 

Errors in Height of Front and Rear Sights. — In 
the previous discussions it has been assumed that the zero 
of the rear sight, and the top of the front sight, are at the 
same distance from the axis of the piece. If this be so, the 
natural line of sight is parallel to the axis of the piece in all 
positions, and hence the vertical plane containing this line 
is likewise parallel to the plane of fire in all positions. 



If, however, the height of the front sight is not the same 
as that of the zero of the rear sight, an error is introduced. 
To show this, in Fig. 273 let A and R 
be the vertical projections of the rear 
and front sights, respectively, and AB 
the horizontal projection of the natu- 
ral line of sight when the axis of the 
trunnions is horizontal. 

Suppose that, due to inequalities of 
the ground, the axis of the trunnion is- 
revolved through the angle 0. 

Then A' and B' will be the verti- 
cal projections of the rear and front 
sights, and A'B' the horizontal projec- 
tion of the natural line of sight. This 
line is now inclined, in its revolved 
position, to the axis of the piece, and 
T hence in the revolved position the 

Fig. 273. plane of sight will intersect *he plane 

of fire. Hence, to an observer behind the gun, if the line of 
sight be directed on the target T, the gun will shoot to the 

This error is similar to that discussed in subject 273. In 
that case it can be removed by keeping the rear sight verti- 
cal. The error in the present case can only be removed by 
making the heights of front sight and of zero of rear sight 

283. Motion of Target 

Rotation of the Earth — Variations in 

The target may move directly toward or from the gun, 
at right angles to the line of fire, or oblique to that line. As 
the last case includes both the others, it will be considered. 

Let AB, Fig. 274, be the line of fire, and BC the direction 
of motion of the target, making the angle <p with the line of 
fire. Suppose the range AB and the rate of motion of the 
object known. 


During the time that the projectile is moving over the 
distance AB the object has. moved over the distance BC. 
Let v denote the velocity of the object and t the time of 
flight of the projectile ; then 

BC = vt. 

Suppose the correction for drift to be such as to cause 
the projectile to strike at B. Then to hit the object the 
correction should be made to cover the additional distance, 

D + CC = D -f vt sin 0, 

in a direction toward the motion of the target. If this 
motion is not known it must be estimated. 

This will still leave a small error in range BC = vt cos 
which must be compensated for by a slight increase in ele- 

Fig. 274. 

vation, or by retaining the elevation corresponding to AB 
and aiming beyond the target the estimated distance BC. 

Rotation of the Earth. — This is not generally taken 
into account. Its effect in the northern hemisphere is to 
cause projectiles to deviate to the right. 

Variations in Ammunition. — The effect of increasing 
the charge and density of loading is to increase the initial 
velocity. That of increasing the weight of the projectile is 
to decrease this velocity, as has already been shown in Inte- 
rior Ballistics. With modern guns these variations in 
ammunition are very slight, and their effects may be neg- 
lected. Variations in moisture also affect the initial velocity, 



a damp powder giving less velocity and a dry powder 
greater velocity, for the reasons previously explained. 

Also the heating of the bore increases this initial velocity, 
since less heat is lost by the gases. ' 

* • 
284. Jump. 

This error is caused by the motion of the gun upon 
discharge, due to the elasticity of tke parts of the carriage, 
the lack of accurate fitting of gun to carriage, the vibration 
of the chase, etc. It varies with different guns and car- 
riages, and is determined by experiment for any particular 
gun as follows : 

In Fig. 275 let AB be a vertical screen or target, placed 

Fig. 275. 

at such a distance from the muzzle of the gun O that it will 
not be affected by the blast. Let OB be the axis of the bore, 
supposed horizontal. The point B where the axis of the 
bore prolonged pierces the target is found by inserting a 
disk in the breech of the gun with a small peep-hole in the 
centre, and placing in the muzzle a pair of cross-hairs whose 
intersection is at the axis of the bore. Looking through 
the peep-hole and at the cross-hairs, the point B is marked 
on the target. When the gun is fired, suppose OA to be the 
line of departure. Then AOB is the angle of jump required. 
The projectile will strike the target at some point C. From 
the triangle A OB we have 

OB~ OB " 

tan AOB. 


From the laws of falling bodies we have 

AC = \gf (403«) 

For the short distance OB we may regard the velocity 
of the projectile as uniform. Denoting this velocity by v, 
and the distance OB by a, we have 


a = vt\ .'. t = —. 

This value of t in (403a) gives 
AC= g A- 

The distance BC to the centre of shot-hole C can be 
measured ; calling this b, we have, for tan A OB, 

tan AOB =^ + -. 

in which the second member is known, since v can be calcu- 
lated by Exterior Ballistics. 

If the shot does not strike vertically above B, there will 

-i c 
be a lateral deviation c, whose measure is tan — . 


If OB is not horizontal, the same principle applies, the 
triangle AOB being an oblique, instead of a right-angled tri- 

285. Description of Sights for 8, 10, and 12 Inch Seacoast Guns. 

These guns have two sets of sights. The first set, AA', 
Fig. 276, is on the middle element of the reinforce, and 
consists of a simple rear-sight notch, A, and a conical front 
sight, A'. They cannot be used for elevations, and are for 
catching the target readily, and giving the general direc- 



The second set, BB ', Fig. 276, is placed on the left 
side of the gun, as shown, and are on this side so as to be 

Fig. 276. 

out of the way of loading, and so that the gun may be 
sighted while the charge and projectile are being inserted. 

The rear sight, Fig. 277, slides 
through a bronze socket, C, bolted to 
the breech-plate. This socket is in- 
clined to the left at the permanent drift 
angle, which is 2° 30' for the 8-inch gun, 
2° 45' for the 10-inch, and 3 00' for the 
12-inch. It is prolonged upward a dis- 
tance ad, to give increased support and 
steadiness to the sight. 

The socket carries a worm, c, which 
engages in a corresponding thread, d, in 
the right-hand edge of the sight. This 
worm is worked by a hand-wheel, e, and 
pinion, e' , and the hand-wheel e is held 
in place, and motion prevented, by a 
clamping-wheel, e". The functions of 
the worm are to raise and lower the rear 
sight, and to hold it fixed in any given 
position, so that it will not be moved by 
the shock of firing. 

The sight consists of a hollow steel 
bar, B, one inch square, graduated in 
degrees, and each degree into six parts. 
The smallest reading on the sight is 
Fig. 277. therefore 10 minutes. The top, a, of the 

bronze socket, C, is divided into 10 equal parts, and the 



divisions on the sight are diagonal, so that by means of the 
scale on the socket, each of these graduations on the sight, 
can be divided into ten equal parts, giving one minute for 
the least reading. 

The top or head of the sight, consists of a deflection-bar, 
g, with a vertical projection, carrying a notch, 1, and a peep- 
sight, 2. The notch is used in connection with the top of 
the front sight, to catch the target quickly, and the peep- 
sight with the cross wires of the front sight, for final adjust- 
ment. Thecleflection-bar, g, has a horizontal sliding motion 
through the top of the rear-sight bar, to correct for wind, 
drift, and other errors, and is clamped in any position by 
the clamp-screw h. It is graduated as shown, each gradua- 
tion being 10 1 60 of the range. 

For deflection to the left, the bar is used in the position 
shown. For deflection to the right the small pin x is pushed 
in, the bar entirely removed from its socket, and reinserted 
from the right, the graduations being the same on the re- 
verse side. 

The right-hand side of the sight-bar, contains a portion, 
of a screw-thread d, into which gears the 
worm, c, for raising and lowering, as 
before explained. 

The front sight B', Fig. 278, consists 
of two truncated cones, with the smaller 
bases together at the middle, and carry- B B 

ing two flat steel cross ribbons, w, halved 
into each other. It has also a top sight 
t, which is used with the open notch of the rear sight B. 

286. Gunner's Quadrant for Mortars. 

When the angle of elevation exceeds 15°, the rear sight 
above described, becomes so long as to be difficult to handle 
and it may bend under its own weight, so as to cause in- 
accuracy in aiming. 

The target, also, in such cases, is not generally visible from 
the gun or mortar, and for these reasons the rear sight is 
not used. To give the necessary elevation in such cases, 
and for mortar-fire generally, the gunner's quadrant is used. 


Fig. 278. 



This consists, Fig. 279, of the body a, and a movable 
arm, b. 

The body is made of bronze, and carries an arc graduated 
on one side from 0° to 44°, and on the opposite side from 
45° to 89°. On the inside edge of the graduated arc are 

Fig. 279. 
teeth c, each of which corresponds to one degree. An arrow- 
is marked on each side of the body, and when the quadrant 
is in use, the arrow on the side on which the reading is taken 
must always point in the direction of the target. 

The movable arm, b, is pivoted to the body at d. 

This arm has a small toothed sector, e, which is acted on 
by a spiral spring, contained in the arm, and by which the 
sector is pressed outward, so that its teeth will remain 
engaged with those of the graduated arc. The upper sur- 
face of the movable arm, b, is the arc of a circle, and on this 
arc rests a level, f. This level bears on the arm at two 
points only, and is of such a length that when moved along 
the arc from its zero-point, to its extreme position at the 
other end of the arm, the angle moved over is one degree. 

The arm is graduated in minutes. 

Degrees are read on the graduated arc, and minutes by 
the scale on the movable arm. 



To Use the Quadrant. — Suppose the elevation to be 
20° 1 8'. 

Press back the toothed sector, e, and move the arm, i>, 
till its index is opposite the 20° mark on the graduated arc. 

Slide the level,/, along the movable arm, b, till its index 
is opposite the 18' mark on. the arm. The quadrant is now 
set to 20 1 8'. 

Place the side, mn, on the flat surface prepared for it, hear 
the breech of the gun, or the side, in it , against the face of the 
muzzle, being careful to keep the side on which the reading 
is taken, to the left, and the arrow, o, pointing toward the 
target. Elevate the piece till the bubble in the level comes 
to rest in the centre. For any elevation greater than 45 u , 
as 6o° 33', use the graduations on the other face of the arc, 
and the scale on the movable arm as above. 

The other side of the quadrant must now be turned to 
the left, and the arrow on it pointed toward the target. 
Elevate the gun as before. 

287. Sights for Siege Artillery — For 7-inch Howitzer. 

The sight for the 5-inch siege-gun, is exactly similar to 
that for the 3.2 field-gun to be described. That for the 
7-inch mortar is the gunner's quadrant already described. 

Sight for 7-inch Howitzer. — This piece has a com- 
paratively low initial velocity, and curved fire. Hence the 
sight for this gun should give a large scale for correcting 
lateral deviations, as thev will be greater than for the siege- 
gun, which has a high velocity. 



Fig. 280. 

Being fired from a fixed platform, the inclination of the 
trunnions may be neglected, in comparison with the errors 
due to low velocity, and hence the standard does not rotate 





about its zero-point, so as to remain always in a vertical 

For the 5-inch siege-gun, its high velocity renders it 
more accurate, and although it is fired from a fixed plat- 
form, and the inclination of the trunnions is consequently 
small, any error due to this cause is eliminated by the rota- 
tion of the rear-sight standard. 

Position. — The sights for the 7-inch Howitzer, (Fig. 280), 
are placed on the right side of the piece, the rear sight, A, 
in a hole drilled through the rear end of the jacket, and the 
front sight, B, on the right rim-base. 

The Rear Sight. — A hole, (Fig. 281), is drilled in the 
jacket, in which fits a socket, b, 
held in place by a set-screw, c. The 
sight is a round steel rod, a, made 
flat on the rear side, which con- 
tains the graduations in degrees, 
and the usual diagonal scale. 

This rod fits accurately in the 
socket b, and carries a sliding collar, 
d, (Figs. 281 and 282), which may be 
fixed at any point along the scale 
by the clamp-screw, e. The rear 
upper edge / of this collar is 
bevelled, and carries a 
means of which the 
diagonal divisions may 
be read to 1 minute. 

The bottom of this 
collar has two projec- 
tions, n, diametrically 
opposite. These fit 
into corresponding 
notches, n' (Fig. 282), 
in the top of the socket 



The axis of these 
notches is at right an- 
gles to the axis of the bore, and they are so arranged that 

Fig. 281. 




the sight may be inserted into the socket for a reading of 
the deflection-bar to the right, or by lifting the sight and 
turning it 180 about its axis, the sight may be reinserted in 
the socket, and the deflection-bar can be read to the left. 
The correction for lateral deviation is /-^-^ 

given by a deflection-bar, h (Fig. 281), / \ 

sliding in a socket, g, on the top of the 
rear sight-bar, and clamped in any posi- 
tion by the clamp-screw *'. It is gradu- 
ated similarly on both sides, and by 
turning the sight 180 , as previously ex- Fig. 283. 

plained, deflections may be read to the right or to the left. 
A vernier, v, on the right edge of the socket, g, enables the 
divisions on the deflection-bar to be read to 
■fo of the scale, the vertical divisions on this 
bar being ^^ of the range. The deflection- 
bar is provided with two movable sight- 
pieces, r and u (Figs. 281 and 283), fitting into 
a socket, s, on the deflection-bar, and held in 
place by a clamp-screw, t. For direct pointing 
the sight piece, r, is placed in its socket in the 
deflection-bar, and u in the front-sight socket. 
For indirect pointing upon an object in rear, 
when the target is not visible, the sight- 
pieces r and u are interchanged. 

Front Sight. — The front sight consists 

(Fig. 284) of a base, a, fastened to the rimbase 

by four screws. 

The top is provided with a socket of the same shape and 

dimensions as that of the deflection-bar h (Fig. 281). The 

thumb-screw d clamps the sighting-piece firmly in position. 

288. Sights for Field Artillery— 3.6 Mortar— 3.2 Field-gun. 

Sights for 3.6 Mortar. — The sights for this piece 

Fig. 284. 




Fig. 285. 



(Fig. 285) are a notch, A, in rear, and a point, B, in front, 

near the muzzle. 

Sights for 3.2 Field-gun. — The rear sight consists of 

a base, A, Fig. 286, which fits in a corresponding socket in 

the gun ; a pivot, B, Fig. 287, 
which fits into the bearing b, 
Fig. 286, of the base, and ro- 
tates around the bearing b, 
Fig. 287 ; and a standard, C, 
Fig. 288, carrying the gradua- 


Fig. 287. 

Fig. 286. 

tions. The pivot B, Fig. 287, has two cuts, c, c', of the shape 
shown, in which slide corresponding projections, c, c' , Fig. 
288, of the standard. 

The cylindrical part, b, of the pivot, B, is held in place 

Fig. 288. 
in the base A, Fig. 286, by two screws, a, a', passing through 



the side of the base. These screws enter slots, a, a', 
Fig. 287, in the pivot B, and allow 
a certain amount of rotation to the 

The standard which carries the 
graduations consists (Fig. 288) of 
an upright bar, C ; a sliding-piece, 
D, moved up and down along the 
bar, C, by a screw, d, and carrying 
the peep-sight, a"; a cross-bar, e, 
carrying the graduations for lateral 
deflection ; a screw, e' , working in a 
half-nut, e', in the pivot B, Fig. 
287, by means of which the stand- 
ard is moved to the right or left; 
a spirit-level,/, which indicates the 
vertical position of the standard; 
and two projections, c, c', which fit 
in the corresponding cuts, c, c', in 
the pivot B. 

The axis of rotation is at the 
zero of the scale, and the usual !>3 
diagonal scale, divided into 10- 
minute intervals, is read to one 
minute, by a scale on the sliding- 
piece D. 

The assembled sight is shown in 
Fig. 289, and its action is evident. Fig. 289. 

Front Sight. — This consists (Fig. 290) of a base, 


a c 





Fig. 2go. 
bolted to the right rim-base ; a standard, b ; and a cylinder, c. 



These are all formed in one piece. The cylinder carries 
two thin cross ribbons of steel, d, in an inner cone, c' , and 
a front sight-point, e. The point e and top of slide d", 
Fig. 289, are used for coarse sighting, while the cross- 
ribbons and peep are for fine sighting. 

The sights are on the right side of the piece. That for 
the 3.6-gun is similar. 

289. Deviations — How Measured. 

Deviations. — Owing to the causes previously explained, 
if a series of shots be fired at a given point of a target, they 
will in general not hit the point aimed at, nor will they be 
grouped symmetrically around this point. Each shot will 
have a trajectory differing from the other shots, and all 
these trajectories taken together will form a sheaf of 
trajectories, whose shape in general is that of a bent 
cone. The- axis of this cone is called the mean trajectory, 
and all the others are grouped symmetrically about it. 
The point where this axis pierces the target is called the 
centre of impact, and the distance of this centre of impact 
from the point aimed at, is called the mean deviation. In 
Fig. 291 let be the point aimed at; AC the axis of the 

Fig. 291. 

sheaf of trajectories ; C the point where this axis or mean 
trajectory pierces the plane of the target. Then C is the 
centre of impact, and OC the mean deviation. 

How Measured. — It is usual to measure deviations in 
three directions : 

1. In the direction of the range; 

2. Laterally, in the direction ab\ 

3. Vertically, in the direction ac. 

For the mean range deviation the target is usually taken 



horizontal, and the measurements made from the centre of 
the target, in the direction of the range. In case a hori- 
zontal target cannot be used, the mean range deviation may 
be obtained from the mean vertical deviation, by considering 
that part of the mean trajectory, CD, in rear of the target to 
be a straight line, making an angle go with the horizontal 
equal to the angle of fall. This angle can be calculated by 
the formulas of Exterior Ballistics. 
We have then 

D'D — CD' cotang w ; 

or, if the mean range deviation is measured on a horizontal 
target, we have for the mean vertical deviation 

CD' = DD' tan w. 

The same method applies to any shot of the sheaf of 
trajectories. The mean lateral deviation is measured parallel 
to ab, and is OD' in the figure, and the mean vertical devia- 
tion is measured parallel to ac, and is CD' in the figure. 
The lateral and vertical deviations of any shot are measured 
in the same way, from the point aimed at, to the centre of 
the shot-hole. 

290. To Find the Centre of Impact — Example. 

In order to measure the mean deviations, it is necessary 
to determine the position of the centre of impact. For this 
purpose, in Fig. 292, assume an origin of co-ordinates at the 

Fig. 292. 

lower left-hand corner O of the target, and axes OX in the 
direction of the range, OY laterally, and OZ vertically. 


The point is selected as an origin, for convenience, to 
avoid the use of negative co-ordinates. 

Let x' , x", etc., denote the distances of the shot-marks 
from measured parallel to OX; 
y',y", etc., parallel to OY; 
z', z", etc., parallel to OZ; 

X', Y, Z', the co-ordinates of the point aimed at; 
X, Y, Z, the co-ordinates of the centre of impact ; 
n, the number of shots. 

x > _f- x» 4- x'" + etc. _ 

X = 

Y = 


y' + y" + y'" + et c- 

_ z' + z" + a"' + etc. 

and the point whose co-ordinates are (XY) in the horizontal 
plane, and (YZ) in the vertical plane will be the centre of 

The mean deviations in range, laterally and vertically, 
will then be 

In range X — X' ; 
Laterally Y - Y ; 
Vertically Z - Z' . 

Similarly for any shot the deviations in range, laterally 
and vertically, will be 

In range x' — X' ; 
Laterally y' — Y' ; 
Vertically z' — Z '. 

In these calculations the positive sign indicates distances 
beyond, to the right, and above the centre of impact ; the 
negative sign distances short of, to the left, and below that 

Example. — Eight shots are fired from the 3.20-inch steel 
field-gun at a vertical target, range 1760 yards. 



Size of target 40 by 20 feet. The co-ordinates of the 
shots, measured from the lower left-hand corner of the target, 
are as given in the table. 

Find the mean deviation in range, laterally and verti- 
cally, or the co-ordinates of the centre of impact. 


Co-ordinates, feet. 

No. of Shots. 







2 1.68 






















Y= 1547 

Z= 7 .8 7 

The co-ordinates of the centre of the target are 
Y' = 20, Z' = 10. 

Hence the mean lateral and mean vertical deviations 
are : 

Mean lateral Y — Y' = — 4.53 feet left ; 
Mean vertical Z — Z' = — 2.13 feet below. 

The mean deviation in range must be calculated. 

In Fig. 293 OA is the vertical height of the point aimed 
at, 10 feet. Assume the angle of fall for this range and 
elevation 00 = 3°.oo, which is very nearly correct. 

The centre of impact C is below the point 0, 2.13 feet. 
Find first the point B, which is the position of the centre of 



the target O on the horizontal plane ; then C , that of the 
centre of impact; and the difference C'B is the mean error 
in range. 
We have 

AB = 10 X cotan 3 = 190.8 feet = 63.6 yards = X' ' ; 

AC = (10 — 2.13) X cotan 3 = 150.1 feet = 50.03 yards = X. 

Mean deviation in range X — X' — — 40.7 feet 

= 13.56 yards short. 

Mean range 1760 — 13.56 = 1746.44 yards. 

Fig. 293. 

291. Errors. 

The centre of impact, as its name indicates, is the centre 
of the group of shots fired, and all the shot are grouped 
symmetrically about it. Hence, if this point be taken as a 
new prigin of co-ordinates, for every positive abscissa or 
ordinate, there must be a corresponding negative one, and 
the algebraic sums of the abscissas or ordinates measured 
from this point, are equal to zero. 

The abscissa or ordinate of any shot measured from the 
centre of impact is called the error. Corresponding to the 
case of deviations, errors are measured in three directions: 
along the range, laterally, and vertically. The distinctions 
between deviations and errors are: 

1. Deviations are measured from the point aimed at ; 
errors, from the centre of impact. 

2. Deviations are not grouped symmetrically about the 
point aimed at unless this point coincides with the centre of 


impact, while errors are grouped symmetrically about the 
latter point. 

It is theoretically possible, by carefully correcting for 
wind, drift, and the various other causes before enumerated, 
to make the centre of impact coincide with the point aimed 
at, and the mean trajectory pass through that point. But 
when this has been done the trajectories will still form a 
sheaf or cone about the mean trajectory as an axis. This is 
due to accidental errors which cannot be corrected, and 
whose consideration requires the application of the doctrine 
of probability, to be discussed later. 

To find the error of any shot, and the mean errors for n 
shot, we have given the co-ordinates of the shot and those 
of the centre of impact, referred to the origin at the lower 
left-hand corner of the target. 

Let X, Y, Z be the co-ordinates of the centre of impact ; 
x', y', z', those of a shot ; 

e x ,e y , e„, the errors in the directions X, Y, Z, respect- 
ively for each shot ; 
e x , € y , e, , the mean errors in range, laterally and ver- 
tically respectively, for n shot. 

e x = x' - X, 

e z = z' — Z, 


e, = 

+ ej + e x " + etc. 
e y + ej + e," + etc. 

_ e x + ej + e." + etc. 

fc , 

The sums e x -\- ej -\- etc., e y -\- e y ' + etc., e, -f- e/ -f- etc., if 
taken with their proper signs, are each equal to zero, accord- 
ing to the principle previously explained. Hence, in adding 
tliese, they must be taken without regard to sign, and the 
sum of their numerical values obtained. For instance, if 



two shots are fired, and one strikes 10 feet beyond and the 
other 10 feet short of the centre of impact, the values of 
e x and ej will be 4- 10 and — 10, respectively, and this sum, 
considering the signs, is zero. 

But the total error committed in this case is 20 feet for 
the two shots, and hence the mean error is -^ = 10. 

The error, measured from the centre of impact directly 
to a shot, is called the absolute error. Denoting this error 
by r, we have 

r=Ve x *+e; or =Ve/ + e/, 
and the mean absolute error is 

, _ r + r, + r,+ etc . 
fc r — 


292. Example. — Find the errors laterally and vertically 
and the mean errors for the 3.20-inch field-gun with the 
data in the last example. 


Co-ordinates — Feet. 

Errors— Feet. 

Squares of Errors. 













4- 1.63 






+ 6.21 

— 2.87 






— 1.22 

— 2.21 






+ 1-53 

— 2.87 













+ 3-53 

4- 1-95 






+ 1-53 







— 0.64 

4- 1. 13 







~2ef— 1 19.4466 



Z= 7 .S7 



It will be observed that the positive and negative lateral 
errors balance each other, and also the positive and nega- 
tive vertical errors, as they should do, for the reasons 


already explained. Also, that the sum of the positive or 
the negative errors in either column, divided by one half 
the number of shots, will give the correct values of e y 
and e,. 

To calculate the range errors and the mean error in 
range, the same principle applies as for deviations, that is, 

e x = e z cotan go, 
e x = e 2 cotan 00. 

In our service a different mean absolute error is some- 
times used as a measure of the accuracy of a gun. It is 
taken as the hypothenuse of a right-angled triangle of 
which the other two mean errors are the sides. Thus for 
the 3.20-inch gun in the example the mean absolute error is^ 

e„, = Ve; + 6 / = 4/(3.20)°+ (1.9875)' = 3-77 feet. 

This differs slightly from the true mean absolute error e r 
previously explained, which would be in this case 4.003 feet. 


293. Division of Sheaf of Trajectories— Law of Error — Probability 
Curve — Principles upon which Form of Curve Depends. 

Division of Trajectory. — Considering the errors in a 
given number of shots, it is found that they vary in magni- 
tude according to a certain law. As we approach the centre 
of impact the shot-marks become more numerous, and as we 
recede from it they decrease in number. That part of the 
sheaf of trajectories which contains one half the whole num- 
ber of shots is called the " nucleus "; outside of the nucleus, 
the surrounding part, containing 40 per cent, is called the 
"envelope"; and outside of this, the remaining 10 per cent is 
called the " tailings." 

Law OF Error. — Since one half the shot are grouped 
within a small distance of the centre of impact, it may be 
inferred that small errors are more apt to occur than large 
ones ; and since only 10 per cent of the shot lie at any 
considerable distance from the centre of impact, it may be 



inferred that the chances of committing large errors are 
small, or that very large errors are not likely to occur. 

Probability Curve. — This law is general and applies 
not only to errors of shot, but to accidental errors of any 
kind. It may be expressed by a curve, called the proba- 
bility curve, whose form is shown in Fig. 294. 

In this figure let represent the centre of impact, and 
XX' the direction of the range. Let Oa, Ob, Oc represent 
errors in range, their magnitude being represented by the 
lengths of Oa, Ob, etc., measured from O. Then from the 
law of error it is evident that the smaller error Oa is more 
likely to occur than the larger one Ob, and this latter than 
the larger one Oc. 

In a large number of shots, the error Oa will also occur 
more frequently than Ob, and so on. 

If in 10 shots the error Oa occurs four times, Ob three, 
and Oc once, the fractions 

tV T 8 7r> tV 
measure the probability of the occurrence of these errors 

Hence if we lay off errors along XX', measuring from 0, 
and at the points a, b, c, etc., erect ordinates proportional to 
the probability of the corresponding errors, we will obtain 
the curve in the figure. 

The same discussion applies to lateral and vertical er- 
rors, as they follow the same law. 

Principles upon which Form of Curve Depends.— 
The form of the curve depends upon the following gen- 
eral principles : 


i. The number of shots striking at will be greater 
than at any other point, or the probability of the error zero 
will be greater than that of any other error, and hence the 
maximum ordinate of the curve will be at 0. 

2. The number striking in the vicinity of will be 
greater than for points farther to the right and left, and 
hence the ordinates of the curve will decrease slowly 
near 0. 

3. The number of hits will decrease rapidly as the dis- 
tance to the right and left of increases, and hence the 
ordinates of the curve will decrease rapidly in these direc- 

4. For great distances from 0, corresponding to large 
errors, the ordinates will be very small, since great errors 
are not likely to occur. 

5. The only error that cannot occur is one infinitely 
great, and hence the ordinate of the curve becomes zero at 
an infinite distance, or the axis of X is an asymptote to the 

6. Since the shot are as likely to fall short of the point O 
as beyond it, the same error Oa is as likely to occur on one 
side of as on the other, and hence the curve is symmetri- 
cal with respect to the axis OY. 

294. Equation of the Probability Curve — Properties of the Curve — 

Equation. — The equation of the probability curve, de- 
duced by analytical methods, is (see Johnson, equation 1) 

j,= *,-*•-, (404) 

in which y is the ordinate of the curve corresponding to the 
abscissa x, or the probability of the error x ; 
h is the modulus of precision, whose meaning and 

value will be explained ; 
it = 3.1416; 

e = the base of the Napierian system. 
Properties of the Curve.— Differentiating equation 
(404) twice, we have 


t—inr" <«> 

^=-^-'-(l~2kV), . . . (406) 

ax* Vn 

From equation (405), when x = o, we have 


and hence the tangent at y is parallel to the axis of x. 
Placing — - t = o, we have 

1 — 2AV = o, 

' = !& (4 ° 7) 

hence -^4 P a sses through zero and changes its sign for the 

value of x given in equation (407). There is therefore a 
point of inflection for the curve corresponding to this 

Limits. — In discussing the probability of making an 
error, it is usual to consider this error as lying within certain 
limits. Hence it is necessary to consider the area bounded 
by the probability curve, the axis of errors, and an)- two 
ordinates whose abscissas represent the limits between 
which the given error lies. The area so determined repre- 
sents the probability of the occurrence of the error within 
the given limits. 

The general expression for the area- of a curve is 

P = Jydx. 
Replacing y by its value from (404), we have 

P=JLf e -™ dx (408) 


The axis of XX' extends to infinity in both directions as 
explained ; hence the total area under the curve will be 
obtained by integrating equation (408) between the limits 
+00 and —00. That is, 

\ nJ — °° 



hx — a, .: dx = -— ; 


P= J 7=f '~*da. (409) 

V 7fl— °° 

The value of the integral between limits is, from calculus, 

/e' a 'da — Vn:; (4 IQ ) 

hence in (409) 


or the total area under the curve is unity. This means that 
it is certain that the error will be contained between +00 
and — co . 

Similarly, for the probability that an error shall be con- 
tained between any limits -j- x and — x, we have 

P = A_r +x e -^ dx (4I1) 

Since the curve is symmetrical with respect to the axis 
OY, we have 

._ h _ r 


Vx -™ dx= ±lLr x e -™ dx . . (4I2) 


for the probability that the error shall be less than x re- 
gardless of its sign. 


295. Modulus of Precision h— Use of Table L 

Assume, equation (404), 

h -wip 

The smallest possible error is zero. Making x = o in 
the above equation, we have 



for the probability of the error zero. It is evident that this 
is the greatest value of y, and gives the maximum ordinate 


Suppose we have another series of shots for which the 
value of h differs from that for the first series, as h' = 2h. 
Then the probability of the error zero in the second case 
will be 

?=^=> (4H) 


and the ordinate will be twice that in equation (413). 

That is, the probability of the error zero will be twice as 
great in the second series as in the first. As the accuracy 

increases with the probability of making no error, we con- 
clude that the second series of shots is more accurate than 


the first. The quantity h is then a measure of the precision 
of the shots, and hence is called the modulus of precision. 

If we construct the probability curves for the two series 
of shots, since the areas under them are always unit}', we 
will have those represented in Fig. 295, OY representing 
the maximum ordinate for the first series and OY' for the 
second. It is evident, from the above discussion and figure, 
that for the same error, x, the curve of probabilities will vary 
with the modulus h. Hence it is usual to change the form 
of the equation for probability, so as to introduce // as a 
factor of the error x, and hence into the limit. Equation 
(412) is therefore generally written 

P^A-^k) (415) 

The values of P for different values of hx have been cal- 
culated and tabulated, and are given in Table I. The value 
of h as deduced analytically is 

In — 1 
V ^2?" 


in which 

n is the number of shots ; 

2e\ the sum of the squares of the errors in any given 
Use of Table I. — Let it be required to find for the 3.20 
gun the probability of committing a lateral error less than 2 
feet, at a range of 1 mile. 

The value of 2e, for this gun is 119.45 (see example, 
Subject 292) ; hence 

h J 


.1711 ; 

k -\J 2 

X 1 1945 

x = .1711 

X 2 = 

.3422 ; 

' for hx = 

.3422 = 


P = 

about ^ ; 

or about four shots in ten will make an error less than 2 feet 
laterally, at one mile range. 


Table I. 






















.045 r 1 












• ■3476 








.57161 j 




.22270 , 











.64938 , 




.32863 1 






■36936 | 



•38933 ' 










1. 00 
i. 08 

1. 10 
1. 12 
1. 14 
1. 16 
1. 18 









0.9 1 03 1 








































































296. Probable Error — True Mean Error — Relation between Prob- 
able and True Mean Errors. 

Among the errors which may be committed, from zero 
to infinity, there are two whose values are of constant use 
and importance. 

These are the probable error and the true mean error. 

Probable Error. — In Fig. 296, the total area under the 
probability curve being unity, if the abscissas Op on each 
side of O be so taken that the area pp'p'p included between 
the curve, the ordinates//', and the axis XX' is equal to one 
half, the error Op is called the probable error. That is, it is 
the error whose probability is one half, or the error which is 
as likely to be exceeded as not. For example, if ten shots be 



fired, and be the centre of impact, the probability is that 
five of these shots will strike within the distance Op from the 
centre of impact and the other five at a greater distance. 
It is to be noted that while the probable error is Op, it may 

occur on either side of 0, and hence it must be measured in 
both directions from O. 

From Table I, the value of hx for P = \ is 

hx = 0.4769. 
Hence, calling this error x t , we have 
_ 0-4769 

Xj, = 


Substituting for h its value from (416), we have 

x p = 0.6745. /J¥- (418) 

True Mean ERROR. — The mean error has already been 
calculated for the 3.20-inch gun for a limited number of 
shots. If the number of shots be increased, a different value 
for the mean error would be obtained, and the true value of 
this mean error can only be found for an infinite number of 
shots : hence the name. Since it is impossible in practice 
to fire an infinite number of shots, the value of the true 


mean error must be found by analytical methods from the 
equation of the curve. This method gives for its value 

X '" = kVn (4I9) 

Substituting the values ol n, and of h from (416), we have 

*m.= 0.79788. —^- (420) 

V « — 1 
Dividing equation (418) by (420), we have 

^ = 0.8453; .-..*> = Q.8453*,.. . . . (421) 

297. Probable Zone — Examples — Comparison of Mean and True 
Mean Errors. 

Probable Zone. — The probable zone is one which will 
probably contain 50 per cent, or one half, the total number 
of shots. Hence the probability for this zone is P=$. 
Now, in considering the probable error, it was shown that 
it measured a distance on each side of the point of impact 
within which one half the whole number of shots would 
strike ; and hence if we lay off a distance on each side of the 
centre of impact equal to the probable error, and draw 
through the points thus determined two lines at right angles 
to the plane of fire and extending indefinitely in both direc- 
tions, these lines will determine a zone which will contain 
50 per cent of the shots. 


Fie. 297. 

In Fig. 297 let be the centre of impact ; x t Ox t , the di- 
rection of the range, or line of fire ; Ox t , measured in both 
directions from O, the probable error. Then the zone de- 


fined by the parallel lines extending to infinity in both 
■directions is called the probable zone, and will contain one 
half the whole number of shots fired. The same reasoning 
applies to "the lateral and vertical probable zones. 

The width of this zone is twice the probable error, or 

■zx p = 2 X 0.6745/1/ - = 1. 349A/ ;■ (422) 

Examples. — Find the probable error, true mean error, 
and probable zone vertically for the 3.20-inch gun at one 
mile range. 

x p = 0.6745^^- = 0.6745^ ^i^ = 1.523 feet ; 

x« = o. 79788a/ — — = o.79788\/^ : ^ = 1.802 feet ; 
2x t = 2 X 1.523 = 3-°4 6 f eet. 

The same method will give the corresponding errors 
and zones laterally and in range, 2e° differing for the differ- 
ent directions. 

Comparison of Mean and True Mean Errors. — The 
true mean vertical error in this case is x m = 1.802 feet, while 
the mean error as obtained from eight shots is (see table) 
1.9875 feet. Hence the mean and true mean errors differ 
very slightly, and with a large number of shots the differ- 
ence would be still less. This is true generally, and hence 
the calculated mean error may be used instead of the true 
mean error without appreciable error in the result. This 
leads to a simple method of calculating probable zones, as 
follows : 

From (421) we have 

*, = 0.845 3*,,, ; .'. 2*> = 1.69*,,. . . . (423) 
Substituting for x, H the calculated mean error e x , e y , or 

5 i6 




e s , we have for the probable zone in any one of these direc- 
tions : 

Range 2x p = 1.69 X e,; \ 

Lateral zy p = 1.69 X e,; >■ . . . • (424) 

Vertical 2z p = 1.69 X e,. ) 

298 25 per-cent Rectangle — Probable Rectangle — Rectangles of 
any Percentage. 

Let 0, Fig. 298, be the centre of impact, XX' the 50 per- 
cent zone for the range, YY' the 50 per-cent zone laterally. 

The intersection of these zones 
will form a rectangle about the 
centre of impact, and this rect- 
angle will contain one fourth or 
25 per cent of the shots, for 

.50 X .50 = .25 

This is called the 25 per-cent 
rectangle. It is the rectangle 
formed about the centre of im- 
FlG - 2 9 8 - pact by the intersection of the 

two 50 per-cent zones; and since each contains 50 per cent 
of the shots independently of the other, by the doctrine of 
probability, when they intersect, their common part will 
contain a percentage equal to the product of the two. 

Probable Rectangle. — The probable rectangle is one 
which is formed by the intersection of two zones of equal 
probability, and which will probably contain 50 per cent of 
the shots. That is, its probability is P = £. 

Now the probability of any rectangle, as illustrated in 
the case of the 25 per-cent rectangle, is equal to the product 
of the probabilities of the two zones whose intersection 
forms the rectangle ; and denoting the probabilities of these 
zones by P' and P" respectively, we have 

P = P'X P". 

It is evident, however, that there are an infinite number 
of zones whose intersection will give a rectangle having the 
probability P=i, since any two, the product of whose prob- 



abilities is one half, will fulfil this condition. To fix the 
rectangle, therefore, we impose the condition that the prob- 
abilities of the two intersecting zones shall be equal. Sub- 
stituting in the above equation this condition, we have 


or the probability of committing an error less than one half 

of either side of the rectangle is P' = P" = S/\. 

P = Vi = 0.7071 

we have, from Table I, 

hx = 0.7438 ; 


_ o-7438 
h " 


Substituting for h its value from (416), we have 

X = I.052\/ . 

V n — 1 

This is the value of one half the side of the rectangle. 

/ 2e* 
V n — 1 

2X = 2.IO4 

Calling the sides of this rectangle in the horizontal plane 
A x and A y , and in the vertical plane A y and ^ s , we have 

A x = 2.1044/ ; 

V n — I 

4, = 2.104*/ — -; 

V n — 1 

A, = 2.104 

v 7 — 

V n — . i 


Rectangles of any Percentage. — By similar reason- 
ing we can find the probable rectangle which will contain 


any given percentage of shots. For instance, required the 
rectangle which will contain twelve out of twenty shots, 
fired from the 3.2 gun at one mile range. 
We have 

£f = 60 per cent. 

The probability of this rectangle must then be 

P = A 

and hence the probability of its sides P' = V.6, since 

V&X V6 = .6 = P. 

From Table I the value of hx corresponding to 

P' = V.6 — .7746 

hx = .8572 ; 


Substituting for h its value from (416), we have 

x = 1. 212 

2x = 2.424 

2y = 2.424. 


V n — 1 

V *=!' 

v « — 1 

V » — 1 

2^ = 2.424 

and so on for a rectangle of any percentage. 

299. Examples — Measure of Accuracy of Guns — Calculation of 
Probable Rectangle from Mean Error. 

Find the 25 per-cent rectangle, the probable rectangle,., 
and the 60 per-cent rectangle for the 3.20 gun, in the vertical 
plane, at one mile range. 


I. The 25 per-cent rectangle: 

The probable zone vertically is (see subject 297) 

2z t = 3.046 feet. 

The probable zone laterally is 

/ ^v" A !9-45 r 

2y t = i.349y ^f^ = i-349y — y- = 5-57 feet. 

Hence the 25 per-cent rectangle is 

3.046 X 5-57 = 16.97 sq. feet. 
2. The 50 per-cent rectangle : 

A y = 2.1044 /- — — = 2.1044/ — ^— = 8.69 feet; 

/ 2e* /l572 
J, = 2.104-1/ — — = 2.1044/ =4.75 feet. 

Hence the 50 per-cent rectangle is 

8.69 X 4-75 = 4 I -3 I s q- f eet. 
3. The 60 per-cent rectangle : 

/ Se % 

21' = 2.4244 / — — = 10.01 feet ; 

V « — 1 

/ 2e* 

2z = 2.4244/ — '— — 5.48 feet. 

V n — 1 

Hence the 60 per-cent rectangle is 

10.01 X 5.48 = 54.82 sq. feet. 

Comparison of Accuracy of Guns. — The probable 
or 50 per-cent rectangle, is generally used to compare the 
accuracy of different guns, and may be taken either in the 
horizontal or in the vertical plane. For small arms and 
high-power guns the vertical rectangle is the more accurate 
means of comparison. It is evident that for high-power 


guns, with flat trajectories, the horizontal rectangles will be 
larger than for guns with high-angle or curved fire. Hence 
if we compare guns and mortars by their horizontal rect- 
angles, the mortar will appear the more accurate. On the 
other hand, for high-angle or curved fire, horizontal targets 
should be used as a means of comparison. The most accu- 
rate method for all guns is to take the plane of the target 
at right angles to the trajectory at the point of impact, but 
this is generally impracticable. 

Calculation of Probable Rectangle from Mean 
Error. — The mean error of a given number of shots may 
be readily obtained as previously shown. 

For the side of the 50 per-cent rectangle we have, equa- 
tion (425), 

4, = 2 * = i*ip_8 (427) 

From (417), 

^ = °-^; (428) 

and from (421), 

x t — 0.845 3*» (429) 

Substituting the value of x t from (429) in (428), we have 
k _ 0.4769 . 

O.845 3*m ' 

and this value of h in (427) gives 

A x = 2x = 2.636 X x m (430) 

300. Use of Probable Error in Calculating Probabilities — Use of 
Table II — Example. 

The probable error is generally used as a standard of 
comparison for other errors, since it represents an error 
which is as likely to be exceeded as not. 

For the probable error we have, equation (417), 

_ 04769 
x * 1 — * 



Using this as a unit of comparison, the ratio of any other 
error x to this is 

x hx 



In Table I we have given, values of P corresponding to 
hx, or, conversely, values of hx corresponding to P. Divid- 
ing the values of hx in Table I by 0.4769, we have the cor- 


responding values of — . 
Finding the values of P, from Table I, corresponding to 

these values of — . we can form a new table, giving the values 
x t 

X X 

of P corresponding to — , or the values of — corresponding 
x t x t 

to P. 

This table is called Chauvenet's Table, and is given 

Table II. 




















• 15 

• 17 

























■ 59 













• «4 








1. 00 





1. 12 

1. 14 

1. 17 

1. 19 












1. Si 







1. 71 



























Use of Table II — Examples. 

1. Required the probability of committing a lateral error 
with the 3.2 gun, at 1 mile range, of less than 4.354 feet. 

The probable error laterally, for this range, is 2.785 feet, 


y t 2.785 

- 4 -345 = I . 56 . 



From Table II, P for ?- = 1.56 is 

P— 0.7071 = VJT 

2. The probable lateral error of the 3.2 gun at 1 mile 
range is 2.785 feet. 

The probability of committing an error less than x, is 
P = Vi — 0.7071. Find the value of x. 

From Table II, for P = 0.7071 we have 


1.56, .-. y = 1.56 X 2.785 = 4.345 feet 

301. Probability of Hitting any Plane Figure. 

By the previous methods it has been shown how to deter- 
mine the sides of a rectangle which will contain any given 
percentage of shots. By the use of Table II we can readily 
determine the probability of hitting any plane figure of a 
given size and shape. 

As the simplest case, consider first a rectangular object. 

























Fig. 299. 

Let O, Fig. 299, be the centre of impact, OF and OZ the 
rectangular axes, and suppose vertical errors to be measured 
along OZ, and horizontal errors along OY. For the given 
gun and range, the probable errors horizontally and verti- 
cally will be known by firing a certain number of shots and 
calculating the probable errors by equation (418). 

1. What is the probability of striking the rectangle 


From Table II we find the probability of committing the 
error OG by taking out the value of P corresponding to 

y* ~ yi 

From the same table we find the probability of commit- 
ting the error OM by taking from this table the value of P 
corresponding to 

OM _ _z_ 

Zp Zp 

and the probability of hitting the rectangle ABCD is the 
probability of committing these two errors simultaneously, 
or the product of the above separate probabilities. 

2. What is the probability of striking the rectangle 

From the fact that the shot are grouped symmetrically 
about O, owing to the law of probability, it follows that the 
number of hits in OGBM will be \oi those in the rectangle 
ABCD. Hence the probability of hitting the rectangle 
OGBM is \ that of hitting the rectangle ABCD. 

3. What is the probability of striking within OMKF ? 

This is found exactly as for the rectangle OMBG. Find 

from Table II the probabilities corresponding to — and 


, and multiply these probabilities together. The result 


will be the probability of striking within the rectangle 
K"KK'K'", and £ of this will be the probability required. 

4. What is the probability of striking FKBG ? 

It is the difference between the probabilities for OGBM 
and OFKM, which have already been found. 

5. What is the probability of striking OGHL ? 

Find from Table II the probabilities for — and ; mul- 

yp Zp 

tiply these probabilities together and take \ of the prod- 
uct for the probability required. 

6. What is the probabilit}- of striking FGHI ? 



It is the probability of striking OGHL minus the proba- 
bility of striking OFIL. 

7. What is the probability of striking IKBH ? 

It is the probability of striking OMBG minus the sum of 
the probabilities of striking OGHL and LIKM. 

In the same way any figure may be divided into rect- 
angles, approximately, whose centres coincide with the 
centre of impact. 

The probability of striking the rectangles or parts of 
rectangles about the centre of impact may be readily calcu- 
lated by Table II, and the probability of striking those parts 
whose centres do not coincide with the centre of impact 
may be determined by subtraction. 

302. Eight-line Method. 

The area under the probability curve being unity, and 
the curve being symmetrical with respect to the axis OY, 

the area under each branch is £. If a right line BC, Fig. 
300, be drawn so that the area of the triangle OBC = £, and 
the abscissa of its centre of gravity be at a distance Om. from 
O, equal to the true mean error x m , then the right line BC 
may be substituted without appreciable error lor the prob- 
ability curve. 

In this case the greatest possible error is OC and the 
greatest possible ordinate is OB, and to show that the right 
line may be substituted for the curve it is necessary to 
prove : 


1. That the probability of the error OC does not differ 
sensibly from that of the error 00 , which is the greatest 
possible error in the case of the probability curve. 

2. That the ordinate OB does not differ sensibly from 
the maximum ordinate OY of the curve. 

1. Probability of the error OC. 

Since in a triangle the centre of gravity is situated at a 
distance from its base equal to \ its height, we have 

OC = 30m; 

but, from (419), 




■* *M — 

_ 3 



ky. OC = hx = — ~ = 1.6925. 


From Table I the value of P corresponding to hx = 1.6925 


The value of P for hx — 00 is 

P— 1.00, 

hence the probabilities of the extreme errors in the two 
cases are as 

.983 : 1. 00. 

That is, out of 100 shots 98 will make an error less than OC. 

2. Value of the ordinate OB, as compared with OY. The 
maximum ordinate OY oi the probability curve is found 
by making x = o in equation (404). The value thus ob- 
tained is 

h hVn 


Vn 71 


or since 

x m = 

we have 

0Y = 




n X x m 


From the triangle OBC, since its area is \ and its base 
$x M , we have 

1 _ {OBx$x m ) , 

2 2 ' 



3 Xx„ 


Comparing (432) and (433), we see that the numerators of 
the values of OY and OB are the sarhe, and the denomina- 
tors differ but slightly, and hence OB may be taken for OY, 
or the right line may be substituted for the curve without 
appreciable error. 

303. Value for Probability by the Eight-line Method. 

In Fig. 301 make 

OC=x" = 3 x m ; 
Ox = x ; 
Om = x m ; 
xx = p'. 


Then the area OBC = — = ^^- . 

2 2 

A^oB^ = {oi±f£)o, = {i±!Ly (434) 

From the similar triangles OBC and xx'C we have 
OB-.OC:: xx' : OC - Ox, or / : x" : : p' : x" - x ; 

P - x „ , 


x" =3x„, 


., _y\ix m -x) 

ix m (435) 

Substituting in (434) for/' its value from (435), we have 

area OBx'x = ^ " *^ x . . . . (43 6) 
®x m 

Now the probability of an error less than Ox = x is the 
ratio of the area of the triangle OBC to that of the trape- 
zoid OBxx'; hence, dividing (436) by the area of the triangle 


, we have 

P = 2 - X - 

3 x m 

1 x' 
~ 9 X, 


In this equation, having the value of the true mean error 
given by the equation (420), or that of the mean error ob- 
tained as explained from a number of shots, we can find the 
probability of any error x without using the probability 

This discussion of probability may be extended to include 
the methods for hitting circles or ellipses, and also for de- 
termining the number of shots necessary to produce a given 
result, such as to make a breach in a wall, etc., but the 
discussion is too extensive for the present course. 



304. Division — Hand Arms — Cutting Arms — Principles — Light 
Artillery Sabre. 

Division. — Portable arms are those which are carried by 
the individual soldier, and are divided into — 
i. Hand arms. 
2. Small arms. 
Hand Arms are those which are used for attack and de- 
fence at very short distances, and are divided according to 
their mode of action into — 
i. Cutting arms. 

2. Thrusting arms. 

3. Thrusting and cutting arms. 

Cutting Arms — Principles. — A cutting arm is one 
which acts by its edge, and, being used entirely against ani- 
mate objects, is based upon the following general principles: 

1. Since the object to be cut is elastic and fibrous, the 
blow must be struck so that only a few points of the cutting 
edge at a time will come in contact with the body, and in 
order to prevent the fibres or the muscles from mutually 
supporting each other, they must be cut one at a time. 

For these reasons the edge of a cutting weapon should 
be curved, and the blow oblique rather than direct. 

The kind of curvature of the edge (convex or concave) 
will depend on the direction in which the weapon is moving 
at the time of the blow. If moving toward the object, the 
edge should be convex; if from it, concave. 

Extreme examples are seen in the Turkish sabre, a, and 
the Arab yataghan, b, Fig. 302. 

2. In order to give force to the blow, the centre of 



gravity should be well forward ; an example is seen in the 


3. For facility of handling, the centre of gravity shou'.d 
be near the hilt. 





Fig. 302. 

As these two principles are conflicting, a compromise is 
generally effected by throwing the centre of gravity well 
forward in a cutting weapon, and well to the rear in a 
thrusting one, and giving it an intermediate position where, 
as in the cavalry sabre, the two functions are combined. 

Light Artillery Sabre. — This is the only distinct cut- 
ting weapon in service, and it has a short curved blade with 
a comparatively light hilt (Fig. 303), the centre of gravity 
being well forward. The cross-section is grooved for 
lightness and strength. 

Fig. 303- 

305. Thrusting Arms — Principles — Straight Sword — Bayonet — Lance 
— Cutting and Thrusting Arms — Cavalry Sabre. 

A thrusting arm is one which acts by its point, and is 
based upon the following principles : 

1. Its penetration depends on the power of the wedge at 
its point, and hence this point or wedge should be as sharp 
as possible consistent with strength. 

2. For a given power of wedge, the penetration also de- 
pends on the position of the axis of the wedge with reference 
to the thrusting force. Hence the blade of a thrusting 


weapon should be straight, to prevent the turning aside of 
the point by the oblique component of this force. 

3. For facility of handling, the centre of gravity should 
be well to the rear, and the blade should be light. 
The principal thrusting weapons are 
The straight sword ; 
The bayonet ; 
The lance or pike. 
The Straight Sword (Fig. 304), as its name indicates, 
has a straight blade and sharp point, and the centre of grav- 
ity well to the rear in accordance with these principles. 


Fig. 304. 

The BAYONET. — This is intended to convert the gun into 
a pike. It was formerly employed very extensively, but its 
use has gradually decreased as ranges and velocities have 
increased. It is still supplied with the latest model guns, 
and is shown in Fig. 305. 

\ u 

Fig. 305. 

It is fixed to the muzzle of the gun by a spring clasp, a, 
engaging over a stud on the upper band, and by a ring, b, 
which encircles the muzzle. 


Fig. 306. 

The older form of bayonet in use on the Springfield 
Rifle cal. .45 is shown in Fig. 306. Its cross-section is 
shown in the figure, and is such as to give lightness and 


The parts are : the blade a, neck or shank b, socket c, 
clasp d, and groove e. Its method of attachment to the gun 
is well known. 

The Lance or Pike. — This is still used in some foreign 
services, and is a sharp steel blade fixed to the end of a long 
wood handle. This handle is provided with a loop at the 
centre of gravity, for convenience in carrying and guiding. 
It has the advantage of greater length than the other thrust- 
ing weapons, but is inconvenient to carry and handle. 

Cutting and Thrusting Arms — Cavalry Sabre.— 
These weapons combine the functions of the other two classes 
and hence exhibit features common to each class. 

The Cavalry Sabre (Fig. 307) is the only weapon of this 

Fig. 307. 

class in service, and the following points may be noted. As 
it is used both for cutting and thrusting, its blade is longer 
and less curved than that of the light artillery sabre ; the 
hilt is heavier, to bring the centre of gravity further to the 
rear, and the hand is better protected by the guard. 


306. Principal Parts — The Barrel — Calibre— Recoil. 

Principal Parts. — The essential parts of all breech-load- 
ing' small arms are : 

The barrel ; 

The receiver ; 

The breech mechanism ; 

The firing mechanism ; 

The sights ; 

The stock and mountings ; 
and for magazine arms 

The repeating mechanism. 


The Barrel — Calibre. — The determination of the cali- 
bre of a small arm involves the consideration of recoil, initiai 
velocity, and various other questions which will be discussed 
in detail. 

Recoil. — Experience has shown that a certain amount of 
recoil can be borne by the soldier without fatigue. The 
fatigue caused by recoil will vary not only with the weight 
of the arm and the velocity of recoil, but also with the 
nature of the powder, the inclination of the small of the 
stock, the area of the stock resting against the shoulder, etc. 

For convenience of carrying and to avoid fatigue the 
weight of a small arm should not greatly exceed 9 lbs. This 
fixes the weight of the barrel, and for a given weight of 
barrel, or of gun, we conclude generally that the fatigue 
due to recoil increases with the velocity of recoil. We have 
for the velocity of recoil while the projectile is in the bore, 
equation (65), Interior Ballistics, 

*' = ?(■+=) 


Since P, the weight of the gun, is fixed by other con- 
siderations, as above explained, the velocity of recoil can be 
reduced only by decreasing the initial velocity v or the 
weight of the bullet/. 

Objections to Decreasing Initial Velocity. — These art; 
obvious. The object of all improvements in modern guns 
is to obtain as great an initial velocity as possible, keeping 
the maximum pressure within safe limits, as this increase of 
velocity gives greater energy, longer ranges, flatter trajec- 
tories, etc., as will be explained. It is evident, therefore, 
that the fatigue due to recoil can only be reduced and kept 
within proper limits by decreasing the weight of the bullet. 

Advantages of Decreasing Weight of Bullet. — Considering 
the equation 

v = -pV + 1})' 

it is evident that for an allowable value of v', since P is 



constant, a decrease in the weight of the bullet /, will in- 
crease the initial velocity v. 

Therefore a decrease in weight of bullet gives a value 
for the recoil which can be easily supported by the soldier, 
and it also increases the initial velocity of the projectile, 
which is the object sought. Whether this increase in initial 
velocity will be advantageous at different ranges depends 
on the manner in which the weight is reduced, and it is 
necessary therefore to consider the best method of doing 

307. Reduction of Weight of Bullet — First Method — Decreasing the 
Length, keeping the Diameter Constant. 

The weight of the bullet may be decreased: 
i. By decreasing its length, keeping the diameter con- 

2. By decreasing the diameter, keeping the length con- 

3. By changing both length and diameter. 

To determine which of these methods is best, assume the 

dv P , ^ 

aJ=M' («8) 


dv , , 

dl dL ( 43 9) 

R = A^ C w f{v)- (440) 

— = gcos 8, (441) 

Equations (438) and (439) are from Mechanics. In (438) 
P is the total pressure acting to produce acceleration, and 
M the mass of the projectile. In (439) v is the velocity of 
the projectile at any time /, and in the present case is the 
initial velocity. Equations (440) and (441) are from Exterior 
Ballistics. In (440) R is the retardation of the projectile 
due to the resistance of the air, and the quantities in the 
second member are all defined in Exterior Ballistics, d and 


W being the diameter and weight of the projectile. In 
(441) v is the velocity of the projectile at any point of its 
trajectory, p the radius of curvature at that point, and 9 
the inclination of the tangent, g being 32.2 ft.-seconds. 

Decreasing Length of Projectile, Diameter Con- 
stant. — In equation (438), 

dt ~M' 

the total pressure P = p' X \nd 2 , p' being the pressure of 

the powder per unit of area ol base of projectile. 

For constant values of /' and d, P will remain constant. 

Hence if the length of the projectile be decreased, the 

diameter being constant, M will decrease, and from equation 

(438) -r, or the acceleration, will increase. 

In equation (439), 

f dv s 

dv . 
since — increases, v, or the initial velocity, will increase. 

In equation (440), 

R = A i;wW>> 

since W decreases while d? remains constant, R will increase. 
This will cause o to decrease for all points of the trajec- 
tory, and hence in equation (441), 

if ■>? 

— = g cos ff. 

p s — . ■■'■- gca&e , 

p will decrease, or the trajectory will be more curved. 

If /', the pressure of the powder per square inch, be 
increased, P in equation (438) will increase, and hence also 

-p. This, in equation (439), will cause an increase in v, but 

since from (440) the retardation is still great, the velocity 


will fall oft rapidly, and from (441) the trajectory will be 
very much curved. 

The results obtained by decrease of weight of bullet, by 
the method of shortening it, and keeping the diameter con- 
stant, are, therefore : 

1. The velocity of recoil is decreased; 

2. The initial velocity is increased ; 

3. The remaining velocity at different points falls off very 
rapidly ; 

4. The curvature of the trajectory is. increased. 

From the 3d and 4th results we conclude that this 
method of reducing the weight of the bullet should not be 

308. Reduction of Weight of Bullet — Second Method — Decreasing 
Diameter, keeping Length Constant. 

In equation (438), 

dv P 

we have as before 

dt ~ M' 

P = p'Xlnd*. 

Suppose p' fixed and d decreased. Then, since the area 

of cross-section of the projectile decreases in this case, P 

will decrease directly with it, and the mass M will also 

decrease directly with the same area, the length being con- 

stant, and hence the ratio ~jt= will not change. The same 

may be shown for an increase in diameter, the length being 

The sectional density of a projectile is -~- (see Projec- 
tiles, subject 164). Substituting for Wits value, we have 
W \ndH6 



= c'l, 

or the sectional density varies with the length. Hence 
when the length is constant, the sectional density is con- 


stant, and from the above we conclude that for the same 
pressure per square inch, and the same sectional density of 
projectile, no increase of velocity is obtained by reducing 
the weight, assuming the same pressure curve in the two 

In equation (440), 


since 739 and v do not change, there is no change in retarda- 
tion, and consequently there is no change in curvature, 
equation (441). 

Therefore the only effect of reducing the weight of the 
projectile by decreasing the diameter and keeping the 
length constant, or, in other words, keeping the sectional 
density constant, when the pressure per square inch /' re- 
mains constant, is to diminish the velocity of recoil. 

Suppose, however, that/' is increased. 

Then in equation (438), 

dt ~ M' 

M, as before, will decrease directly with the area of cross- 

. . P 

section, but P will increase, and hence the ratio -^ will 

increase. This will cause —r to increase. 


In equation (439), 

C dv J 

v will increase. In equation (440), 

R remains constant, since ^= does not change ; or it may 

even decrease, owing to the increase in v, and the conse- 


quent change in the exponent of f(v) from 3 to 2 (see 
Mayevski's experiments, Exterior Ballistics), v therefore 
will be greater for all points of the trajectory, and in 
equation (441), 

P= T, 

g cos 

p will be greater, and hence the curvature of the trajectory 
will be less, or it will be flatter. 

Hence by decreasing the weight of the bullet by the 
second method, that is, by reducing the diameter and keep- 
ing the length constant, and at the same time increasing the 
pressure per square inch of the powder-gas, we obtain : 

1. A decrease in velocity of recoil; 

2. An increase in initial velocity ; 

3. No increase in retardation, and perhaps a reduction ; 

4. A flatter trajectory. 

309. Reduction of Weight of Bullet— Third Method— Changing 
Length and Diameter — Smokeless Powder — Advantages of 
Reduction of Calibre — Flatness of Trajectory. 

The method at present adopted is to vary the pressure 
per square inch, the length, diameter, and weight of projec- 
tile, so as to obtain the best ballistic results. This has led 
to a reduction of the calibre from 0.45 to 0.30 inch, a de- 
crease in the weight of the bullet from 500 to 220 grains, 
the length being very slightly changed, and an increase of 
pressure per square inch from a maximum of 30,000 lbs. to 
a maximum of 45,000 lbs. per square inch, an increase of 
initial velocity from 1300 to 2000 ft. -seconds, with a reduc- 
tion of velocity of recoil from 14 to 9.6 ft.-seconds, and of 
•energy of recoil from 27 to 11 foot-pounds. 

Smokeless Powder. — It is evident that to obtain any bal- 
listic advantage from a reduction of calibre, the pressure per 
square inch on the projectile must be increased. When the 
calibre of small arms was first reduced, various attempts 
were made to obtain this increase of pressure by the use of 
the old black powder in various forms, such as larger charges 
compressed, slower burning, etc., but the results were un- 



favorable, giving high and irregular pressures, increase of 
fouling, etc. The effort to overcome these difficulties led 
to the introduction of smokeless powder. Its advantages 
have been explained in High Explosives, one advantage of 
great importance being that, as the smokeless powder burns 
more slowly and regularly, it acts upon the projectile like 
the slow-burning powders already described in large guns, 
and hence for a given initial value of p' we obtain a greater 
initial velocity than would be produced by the same initial 
value of/' with the old black powders. 

Advantages of Reduction of Calibre.— The princi- 
pal of these are : 

i. Flatness of trajectory, and increase of range ; 

2. Decrease in weight of cartridges ; 

3. Increase of accuracy of fire ; 

4. Decrease of recoil ; 

5. Increased penetration. 

Flatness of Trajectory. — The advantage of this may 
be illustrated as follows : Assume, equation (441), 

P — 

g cos ff 

Let H, Fig. 308, be the height of a man, and suppose 
this height to be the maximum height of the trajectory. 
The total range in this case is called the maximum contin- 
uous dangerous space, and is frequently used in comparing 
the ballistic qualities of guns. 

The value of cos 6 = 1 at the summit of the trajectory; 

p = — 

for this point. It is evident that p increases rapidly with v. 

Hence for a low velocity we will have the trajectory 

AB, and for a high velocity, A'B', the maximum continuous 


dangerous spaces being- the horizontal distances AB and A'B' 
respectively. The flat trajectory, then, gives a greater con- 
tinuous dangerous space A'B', and this is true when the 
dangerous space is not continuous, as in the case of the ob- 
ject H'; the dangerous spaces being H'B and BB' respect- 

An error in estimating distance is also of less importance 
with a flat trajectory ; as in the figure, an error H'B for the 
curved trajectory, and BB' for the flat one, may be com- 
mitted, and the target will still be struck. The distances 
AB and A'B' for the calibres .45 and .30 are 418 and 600 
yards respectively. 

310. Advantages of Reduction of Calibre — Decrease in Weight of 
Cartridges — Increase of Accuracy of Fire — Increased Pene- 

Decrease in Weight. — The number of rounds carried 
is limited by the physical endurance of the soldier, just as 
the weight and recoil of his piece are fixed by the same 
conditions. A reduction in the weight of the cartridge in- 
creases the number of rounds that can be carried, and this 
increase is very important owing to the great increase in 
rapidity of fire with modern breech-loaders, and the dif- 
ficulty of supplying the fighting-line with fresh ammunition. 
This reduction in weight is due not only to the reduction 
in calibre, but also to the introduction of smokeless powder, 
by which the weight of the charge has been reduced nearly 
one half. 

Increase of Accuracy of Fire. — Owing to the greater 
velocities at all points of the trajectory, the small-calibre pro- 
jectile is less affected by the wind and other deviating causes, 
and the drift is not greater than with the old projectile. 
Hence the horizontal deviations are less than with the old 
projectile. As has already been shown, the flatness of trajec- 
tory makes it more accurate in a vertical direction, and hence 
its absolute accuracy, which is taken to be the radius of the 
circle containing one half the whole number of shots, is 
greater than with the old bullet, the radius of the circle 
being less. 


There is, however, one exception to this. Owing to the 
relative increase in length of the new bullet, it is necessary 
to give it greater velocity of rotation about its longer axis 
to insure stability, and hence the pitch of the rifling is more 
rapid for the new small calibre. 

This increases the passive resistances in the bore, and, 
with the greater pressure per square inch on the projectile, 
causes increased vibration of the barrel. The result is that 
for short ranges the accuracy of the small calibre is slightly 
less than that of the old arm. 

Beyond these ranges the small calibre is more accurate. 

Increased Penetration. — This is due to increase of 
velocity, and also to the fact that the exterior of the bullet 
is covered with a jacket of harder metal, such as copper, 
German silver, or nickeled steel. This jacket holds the 
projectile together and prevents deformation on striking. 
It is stated that the bullet of the 8-mm. rifle has pierced a 
tree 17 inches in diameter, and afterwards passed through 
the bodies of five men. The penetration of the cal. .30 bullet 
with steel jacket is in sand 14 inches, and in oak from 16 
to 24 inches, the target being 3 ft. from the muzzle. The 
penetration of the cal. .45 bullet under the same circum- 
stances is 3.3 inches in oak. 

Numerous experiments have been made upon human 
bodies to test the effect of the small-calibre bullet, with the 
general result that the wounds are less serious and the shat- 
tering effect on the bones less than with the old projectile. 
The shock or stopping power is also less as the calibre 
decreases, unless the bullet acts explosively, and hence it has 
been proposed for the very small calibres to remove the 
jacket from the point of the bullet, thus causing it to spread 
out in front on striking. 

311. Disadvantages of Reducing the Calibre. 

The principal of these are: 

1. The decrease in weight of bullet, and hence the rela- 
tive increase in its length, necessitates a more rapid twist of 
rifling to give it stability in flight, and this increase of twist 
increases the passive resistances in the bore and gives rise 


to greater vibrations of the barrel. These vibrations, as 
stated, decrease the accuracy for short ranges. A test with 
the barrel confined in a fixed rest showed greater inaccuracy 
at 500 yards than with the cal. .45. A heavy barrel cal. .30, 
made expressly for the purpose, was then tried in the fixed 
rest under similar conditions, and remarkable accuracy, 
greater than ever before recorded, was obtained. This 
shows that the inaccuracy is due to vibrations of the barrel, 
and it is probable that when the gun is fired from the 
shoulder in the ordinary manner the targets will be much 
better than when a fixed rest is used, as the barrel in this 
case will not be rigidly held, and consequently its vibrations 
will be less. 

The increase in twist also renders the projectile more apt 
to strip in the bore ; that is, to be forced across the lands 
without taking the rifled motion, with the result that the 
bore is scored or fouled by the metal, and the projectile 
rotates about its shorter axis in flight, or tumbles. This 
has been remedied by the use of a harder metal jacket. 

2. The cleaning of the bore is more difficult. Since the 
introduction of smokeless powder this objection has less 

3. The manufacture is more difficult. 

This has been a serious objection, as it is a very difficult 
operation to bore and rifle accurately such a small calibre, 
and any inaccuracy here is fatal to the accuracy of fire. 
This difficulty has also been overcome, and guns below 0.30 
calibre are now successfully made. 

4. The pressure in the bore is greater. 

The necessity for this has been shown, and it has been 
difficult to provide steel of sufficiently high elastic qualities 
to withstand this pressure. It has also caused the abandon- 
ment of nearly all the old forms of breech mechanism, in 
order to obtain a secure fermeture. 

In spite of these objections, the great advantages of a 
reduction of calibre have led to its universal adoption in all 
countries, and the tendency now is to go below the .30 
calibre. This has been done in some countries. One of 
the points still in doubt is the effect of the small-calibre 


bullet upon the nervous system, and whether a wound from 
this bullet, when not fatal, will stop a man. 

This can only be solved in actual war, and hence in our 
service it has been thought best not to go below the cal. .30 
at present. 

312. Rifling— Pitch — Number of Grooves and Lands — Width — 
Depth — Direction of Twist. 

Pitch. — The pitch of the rifling in small arms is always 
uniform, because, when fired, the bullet is molded accurately 
into the grooves and lands, and the length of the surface of 
the bullet in contact with the bore is great. If the pitch be 
uniform, no change of form of the molded surfaces takes 
place during the passage of the projectile from breech to 
muzzle ; if the pitch be increasing, a change of form is con- 
stantly occurring, resulting in increased resistance, deform- 
ation of projectile, and inaccuracy. 

It has been found necessary in practice to increase the 
twist as the calibre decreases, as alread}- explained (see sub- 
ject 163). 

In the Springfield cal. .45 the twist is one turn in 48.9 
calibres, in the new cal. .30 it is one turn in 33^ calibres, or 
one turn in 22 and 10 inches respectively. 

Number of Grooves and Lands. — The number of 
grooves has no effect apparently upon the accuracy of fire, and 
hence for convenience of manufacture, cleaning, and strength, 
these are as few as possible. The cal. .45 has three grooves 
and lands, the cal. .30 four. As a general rule the number 
has varied from three to seven. 

Width of Grooves and Lands. — The width depends on 
the kind of bullet. When of hardened lead, the bullet is 
slightly upset by the shock of discharge and forced into the 
grooves, the lands cutting into the projectile. As this metal 
offers comparatively little resistance, and the twist is not 
rapid, the grooves and lands in the cal. .45 are of equal width. 

With the jacketed bullet, the resistance to deformation 
being much greater, the grooves are wider and the lands 
narrower, since these latter do the work of cutting into the 


projectile. In the U. S. cal. .30 the grooves are three times 
the width of the lands. 

Depth of Grooves and Lands. — If the depth of groove 
is too great, there is too much work lost in forcing the projec- 
tile, and the forcing may not be perfectly accomplished. 
This latter will cause erosion and inaccuracy. If the depth 
is too small, the groove may be easily filled by fouling. The 
depth also varies with the kind of bullet. The depth of 
groove in the Springfield cal. .45 is .005 inch, and in the 
cal. .30 it is .004 inch. 

The exterior diameter of the lead bullet is 0.457 inch, 
that of bore at bottom of grooves .455 inch (see Fig. 309). 

Hence with the Springfield rifle, in addition to the work 
done by the lands in cutting into the projectile, the latter 
exceeds the diameter of the bore at bottom of grooves by 
.002 inch. This, added to the upsetting action of the pow- 
der, gives a very energetic forcing, and insures its accom- 
plishment, but without great strain on the gun. The 
cannelures or grooves in the bullet also assist in reducing 
the work. With the cal. .30 the exterior diameter of the 
bullet is 0.308 inch, and that of the bore at the bottom of 
grooves the same. Hence the bullet exactly fills the bore 
from groove to groove, and there is no forcing in the 
grooves, aside from what may be due to upsetting of the 
metal by the action of the powder and the pressure of the 

309- Fig. 310. 

In general the grooves have the same depth from breech 
to muzzle. In the case of the Martini-Henry rifle recentlv 
used in the English service, the depth of groove decreased 



from breech to muzzle, to make the forcing more gradual, 
and thus decrease the pressure at the origin, ana conse- 
quently the vibrations. 

Figs. 309 and 310 show the cal. .45 and cal. .30 grooves 
in section. 

Direction of Twist. — This has no influence upon the 
accuracy of fire, as it produces " drift," which can be allowed 
for. All small arms are rifled with a right-hand twist, and 
the resulting drift is to the right as already explained. 

A case occurs in the French service, where the vibrations 
of the barrel, owing to the peculiarity of the breech mech- 
anism, caused the bullet to deviate to the right, and to 
correct this the gun was rifled with a left-hand twist. 

313. Profile of Chamber — Thickness and Length of Barrel. 

Fig. 311. 

Profile of Chamber. — The chamber is made slightly 
conical to facilitate the extraction of the cartridge-case. 
That for the cal. .30 rifle is shown in Fig. 311. The chamber 
must be free from all cuts or scratches, since the cartridge- 
case will be forced into them on firing, and will either stick 
or rupture. All dimensions must be exact, and very little 
variation can be allowed. 

Thickness of Barrel. — The case is that of a single 
cylinder under extension, the exterior pressure being zero 
(see " Elastic Strength of Guns "). For the thickness of the 
cal. .30 rifle-barrel just in front of the powder-chamber, 
assume, equation (205), 

/?,-/?„ = R, 

( FK±ML \ 
• VV 3*. - 4/^ )• 


We have 

/? _-3°_ IC 
*.- — -.15, 

6 a = 61,500 lbs., 
P a e = 40,000 lbs., 

which values substituted in the above equation give 
R l — R — .3429 inch = 1.14 calibres. 

The actual thickness is 0.34 inch = 0.49 — 0.15 = 0.34. 

For the thickness at various points along the bore the 
pressure curve must first be calculated, but other considera- 
tions, such as stiffness to resist vibrations and to prevent 
bending in service, etc., enter, and the exterior is given the 
general form of a conical frustum, the thickness at the 
muzzle being 0.53 calibres, 0.16 inch. 

Length of Barrel. — This is so adjusted that the rear- 
rank man can fire over the shoulder of the man in front 
without danger to the latter, and for the small-calibre rifle 
this length is fixed at 30 inches (100 calibres). 

Experiment shows that increasing this length gives very- 
little increase of initial velocity, while it increases weight 
and difficulty of manufacture. The length of the cal. .45 
barrel is 32.6 inches. The length of travel of the projectile 
in the bore for the cal. .30 is 28.19 inches (94 calibres), and 
for the cal. .45, 30.445 inches (67.6 calibres). 

314. The Receiver — General Features — Receiver for Springfield 

The Receiver is a distinctive feature of breech-loading 
small arms, and forms an extension of the barrel, for the 
purpose of receiving the cartridges and breech mechanism. 

General Features. — The shape of the receiver depends 
on the breech mechanism, and also upon whether the gun 
is a single-loader or a magazine arm. 

In general it must have the following features: 

1. A method of attachment to the barrel. 

2. A method of attachment to the stock. 



3. An opening through which cartridges are inserted, 
empty shells extracted, and in which the breech-block or 
bolt works. 

4. An axis about which the block rotates, or guide- 
grooves for regulating the motion of the bolt. 

5. A recess or groove for locking the block or bolt. 

6. An arrangement for ejecting empty cartridge-shells ; 
and for a magazine arm in addition to the above — 

7. An opening for the admission of cartridges from the 

8. A " cut-off " by which this opening may be used or 
not at will. 

Receiver for Springfield Rifle. — Fig. 312 shows the 
receiver for the Springfield rifle. 

Fig. 312. 

It is attached to the barrel B by the screw-threads a ; to 
the stock, by a screw, b, passing through the tang c ; d is 
the opening through which the cartridges are fed, and in 
which the breech-block works ; H is the axis about which 
the breech-block rotates; g, the recess into which the breech- 
block is locked by its cam-latch, to be described ; / is the 
ejector spring and spindle. The cartridge-case is loosened 
in its seat by the positive action of the extractor E, which 
rotates in the direction of the arrow. The axis of the 
spindle of the spring / is at first above the axis of rotation, 
H, -of the block and extractor. After a small rotation of E, 
the axis of the spindle is carried below the axis H, and the 
spring / then acts to rotate E quickly, and throw out or 
eject the empty case. As the case moves backward, it 
strikes the inclined stud J, and is, by it, deflected upward 
out of the receiver. 


315. Receiver for Cal. .30. 

This is shown in Fig. 313. 

It is attached to the barrel by a screw-thread, and to the 
stockby the screws Jf and Fpassing through the trigger-guard 

Fig. 313. 

into it from below (see Fig. 336) ; z is the opening through 
which the cartridges are fed when the gun is used as a 
single-loader, and z' when used as a magazine arm. The 
left side, r, of the opening z, is parallel to the axis of the 
bore and, together with the surface, r', on the right, forms 
a guide for the bolt when moving forward or back. A 
second groove, k, forms a recess for the operating-handle of 
the bolt to rest in, when this handle is rotated to the right 
in closing the breech. The forward shoulder or cam, s, in 
front of the groove, h, is so shaped as to give a screwlike 
motion to the bolt in closing, thus moving it slowly forward 
to its seat against the breech. The rear shoulder, t, arrests 
the forward motion of the bolt in closing. A third groove, 
k, prevents the firing mechanism from turning with the bolt 
in closing the breech. 

The groove a locks the bolt, a lug on the latter entering 
it. When in the firing position, the pressure of the gas is 
transmitted to the surface of the groove a ; the surface s, and 
the rear surface of the groove h, acting as safety-supports. 

The empty shell is ejected as follows: The bolt is drawn 
slowly backward at first, by the action of the inclined sur- 
face, t, of the groove ^.against the operating-handle. The 
extractor, which is on the bolt, and engaged with the rim 
of the cartridge, draws the case back slowly, due to this 
motion of the bolt. When the bolt is free to move along 


the axis of the receiver, it moves quickly, drawing back the 
empty case. 

At the end of the travel of the bolt, the short arm, e, of 
the ejector-lever, in the bottom of the receiver, is struck by 
a shoulder at the end of a groove in the bolt, and the long 
arm, J, is thrown up, striking the empty case and ejecting 
it. The opening m is the magazine, which will be explained 

The cut-off for the magazine, Fig. 314, is a pin or rod,, 
the rear part, a, of which is round, and the front part, c, is 

cut away partly, as shown. The 
cut-off is inserted in the left-hand 
side of the receiver, parallel to 
its axis (see Fig. 313, C), the cut- 
away portion, c, projecting over 
the opening z 1 of the magazine. 
When the magazine is in use, the flat part of the cut-off 
forms a portion of the surface z' of the magazine opening. 
When the magazine is to be cut off, the rod is rotated by 
turning the handle C. This brings the rounded part of c 
into such a position that it projects into the opening z' and 
forces the cartridges down slightly, so that the bolt will 
pass over without touching them. 

The cut-off is held in the open or closed position by the 
spring C, which works in a groove in the receiver. 

316. Breech Mechanism — General Classification — Sliding Mech- 

The functions of the breech mechanism are to open, close, 
and lock the breech, extract the empty cartridge-case, and 
for magazine arms, in addition, to operate the repeating 
mechanism, and insert the cartridge. 

General Classification. — Breech mechanisms may be 
classified generally into : 

1. Those which operate by sliding. 

2. Those which operate by rotation. 

Sliding Mechanism. — The sliding may take place — 
1. By the motion of the barrel parallel to its axis. 


This arrangement is now obsolete, and is unsuitable for 
a. military weapon on account of the weight of the barrel. 

2. By the motion of the breech-block parallel to its axis. 
Guns with this mechanism are called bolt-guns, and the 

mechanism resembles in its action the bolt of a door, whence 
the name. All magazine arms at present in use belong to 
this system. It presents the following advantages : 

a. Extreme simplicity, great strength, and small number 
■of parts. 

b. Secure locking against the effects of discharge. 

c. Ease of extraction of empty case. 

d. Better adapted to magazine arms than any other sys- 

The objections to the system formerly were : 

a. Danger of blowing out the bolt by premature dis- 
charge, before the breech was securely locked. 

b. Liability to explode the cartridge when pushing it 
home, either by striking it a blow, or by the projection of 
the firing-pin striking the primer in the cartridge-case. 

These objections have been overcome. 

3. The block may slide at right angles to the axis of the 
barrel. An example in seen in the Krupp fermeture. 

The advantage of this system is that it is not liable to 
blow out,, as the direction of the pressure is normal, to the 
bearing surfaces of the block ; the disadvantages are that it 
tends to guillotine the cartridge, does not push it home, and 
renders extraction of the empty case difficult. 

317. Rotating Mechanism. 

The rotation may take place — 

1. Around an axis parallel to the axis of the gun, and at 
one side. This is now obsolete. 

2. Around an axis parallel to the axis of the gun, and 
below it; example, revolvers. 

This system, is objectionable for a military arm, on 
account of the weight of the revolving cylinder, and also 
because of the break in the barrel at the junction of the 
cylinder and barrel proper, through which gas may 


3. Around an axis at right angles to the axis of the gun, 
above that axis, and at the front of the block ; example, the 
Springfield rifle cal. .45. 

This system has the following advantages: 

a. The block acts to push the cartridge home in clos- 

b. It forms, in connection with the extractor, a strong 
lever for extracting the empty case. 

c. It is simple and has comparatively few parts. 
Its disadvantages are : 

a. It does not securely and positively lock the block, and 
the tendency of the pressure is to force it strongly against 
the breech-recess ; hence for high pressures, as in the present 
small calibre, it is difficult to open after firing. 

b. It is not adapted for a magazine arm. 

4. Around an axis at right angles to the axis of the bore,, 
above that axis, and in rear of the block ; example, th& 
Martini-Henry recently used in the English service (Fig.. 

Fig. 315. 

The advantages of this system are: 

a. It is simple and solid, and the block is well protected 
against accident. 

b. The pressure does not tend to blow open the block. 
Its disadvantages are : 

a. A space must be left between the front of the block: 


and the rear of the chamber to allow for rotation of the 
block, and hence the chamber cannot be tightly closed. 

b. The extraction of the empty case is difficult. 

c. The block is liable to guillotine the cartridge, unless 
the latter is forced completely home before closing the 

5. Around an axis at right angles to the axis of the gun, 
below that axis, and in front of the block; example, the 
Remington, Fig. 316. 

Fig. 316. 

This system is simple, but requires an exact adjustment 
of all the parts, especially of the hammer, as in addition to 
its ordinary functions it locks the breech-block. 

A system is also used in which the barrel rotates about 
an axis at right angles to the bore and below that axis ; 
example, shot-guns. This is not used for military arms, on 
account of the weight of the barrel. 

318. Requirements of a Good Breech Mechanism. 

A good breech mechanism should fulfil the following 
requirements : 

1. It should be simple, strong, and safe in action, and 
should work freely under all conditions which are liable to 
prevail in active service, even when rusty or covered with 

2. It should be easy to clean, take apart and assemble, 


and should be composed of few pieces, which are not liable 
to break or work loose, and which are interchangeable. 
Screws are objectionable, as they are liable to work loose. 

3. -The motions in loading should be as few as possible, 
and executed in regular order, and it should be impossible 
to fire the gun till the breech is securely locked. 

4. To increase the rapidity of fire, the motion of opening 
and closing the breech should cock the firing mechanism. 
In general it is preferable to cock the firing mechanism by 
the motion of opening the breech, as this withdraws the 
firing-pin so that it will not strike the primer of the cartridge 
when the latter is pushed home, and in addition, if the mech- 
anism is cocked in closing, a slip of the hand before the bolt 
is home will cause the latter to spring back, and either 
throw out the cartridge which is partly introduced, or, in 
case of a magazine arm, it may cause the introduction of a 
second cartridge before the mechanism, and thus produce 

5. The opening of the breech should automatically eject 
the empty case. 

6. The working of the mechanism should cause as little 
fatigue as possible to the firer. 

7. A safety-device should be provided which can be 
readily seen and operated, and by which the mechanism can 
be locked in place and accidental discharge rendered im- 

8. It should be impossible to strike a blow on the car- 
tridge, either by the bolt, or by the firing-pin, while the 
breech is being closed. 

319. Breech Mechanism of Springfield Rifle, Cal. .45. 

This mechanism belongs to the system in which the 
block rotates about an axis perpendicular to the axis of the 
gun, above that axis, and in front of the block. 

Although it is to be replaced by the cal. .30, the arm is still 
(1895) in service, and is likely to be used in any emergency 
arising within the next few years, and hence its mechanism 
will be explained. 



The principal parts are (Fig. 317): 
The breech-block D ; 
The hinge-pin H; 
The cam-latch G ; 
The extractor E ; 
The ejector spring and spindle I. 


Fig. 317. 

The receiver and ejector spring, spindle, and stud have 
been previously explained. 

The Breech-block. — This has an oblique hole,/, Fig. 
318, through it for the firing-pin. In 'front is the hinge-pin 
hole h, which is elongated parallel to the axis of the bore, 
and through which passes the hinge-pin H, Fig. 317, around 




f h K 

■-*&" *■ 

Fig. 318. 

which the block rotates. In rear is a recess, k, called the 
cam-latch recess, for the cam-latch G and its spring K, Fig. 
317. The shaft of the cam-latch passes through the hole^-'. 

The Hinge-pin. — This forms the axis about which the 
block rotates. It passes through two holes in the lugs of 
the receiver, and is kept from turning by an arm with a stud 
which fits in a hole on the side of the receiver. 

The Cam-latch. — This locks the breech-block in firing 
by entering a circular recess, g, in the breech-screw C, Fig. 
317. It is fixed to a shaft one end of which passes through 
the hole^ - ', Fig. 318, in the block, and the other end is sup- 


ported b}' the breech-block cap g", which is removable. 
The axis of the cam-latch shaft projects on the right-hand 
side, and to it is attached a thumb-piece by which the cam- 
latch is operated. This axis fits loosely in the hole g' in the 
breech-block, and also in the corresponding hole in the 
breech-block cap^-". 

The cam-latch is pressed to the rear into its recess in the 
breech-screw by the cam-latch spring K. 

The Extractor. — This is mounted on the hinge-pin, on 
the left side of the chamber. Part of its lower extremity is 
cut into such a shape as to form, when in place, a part of 
the counterbore of the chamber, in which the rim of the 
cartridge rests. It has also in front, and slightly above the 
axis of the hinge-pin, a recess for the reception of the head 
of the ejector-spindle; and a lug, e, Fig. 317, projects be- 
yond the upper surface of the receiver, against which the 
breech-block bears in opening. 

Action of Mechanism. — When the piece is fired, the 
breech-block slides bodily to the rear, owing to the elonga- 
tion of the hinge-pin hole h, Fig. 318. Owing to this motion 
of the block, and to the loose fit of the cam-latch shaft in its 
holes in the block, the pressure of the powder-gas is trans- 
mitted directly, through the breech-block and the body of 
the cam-latch, to the breech-screw C, and there is no strain 
upon the hinge-pin H or the cam-latch shaft. The block is 
opened by pressing the thumb-piece forward, which dis- 
engages the cam-latch from its recess. When the block 
has nearly completed its rotation upward, it strikes against 
the projecting lug, e, of the extractor E, Fig. 317, and rotates 
the latter slowly, thus extracting the empty case. The 
ejector then acts as before explained, and throws the case 
out of the receiver. 

320. Breech Mechanism of the Cal. .30 Rifle— The Bolt. 

This mechanism belongs to the system in which the 
block slides parallel to the axis of the bore, and the gun is 
a bolt-gun. 

The principal parts are : 



The boltZ>, Fig. 319 ; 
The sleeve /, Fig.' 320; 
The extractor E, Fig. 321. 
The Bolt, Fig. 319, is a hollow cylinder, closed at the 
front end except a small opening,/', in the centre, for the 

Fig. 319. 

passage of the point of the firing-pin. Its interior shape is 
shown in section, Fig. 336. 

The head of the cartridge rests against the front of the 
bolt, which is hollowed to receive it, and which supports 
the pressure of the powder-gas. a is the locking-lug, which 
engages in the locking-recess a, Fig. 313, in the front part 
of the receiver ; r is the guide-rib which rests against the left 
side, r, of the guide-groove, Fig. 313, when the bolt is un- 
locked and rotated, and guides the motion of the bolt. It 
also forms a stop to limit the motion when the bolt is 
rotated in opening. The guide-rib has a shoulder, e, in front, 
against which a corresponding shoulder on the extractor 

The rear end, s, of this rib rests in front of a correspond- 
ing shoulder, s. Fig. 313, on the receiver, when the block is 
locked for firing, and forms a safety-support to resist the 
pressure, the lug a being the first support. D is the body 
of the bolt, in one piece with the operating-handle h. This 
handle terminates at the bolt, in a collar, d, Fig. 319, which 
only partly encircles the rear end of the bolt. 

This collar serves to connect the bolt with the other 
parts of the mechanism. 


The rear side, h', of the operating-handle h, rests in front 
of a corresponding shoulder, h, Fig. 313, in the receiver in 
the firing position, and forms a second safety-support to re- 
sist the pressure. 

At the rear end of the bolt is a notch, k, one side be- 
ing straight and the other inclined. This notch cocks the 
firing-pin when the bolt is rotated in opening, and also 
allows the cocking-piece, carrying forward the firing-pin 
and striker, to move down into it, when the piece is dis- 
charged, as will be explained 

There is also a longitudinal groove,/, its rear end turn- 
ing to one side, and its front end terminating abruptly in a 

This groove works the ejector-lever J, Fig. 313, in the 
bottom of the receiver. The notch i ' admits a stud, i ', Fig. 

320, on the sleeve, and the notch / is for the safety-lock /, 
Fig. 320. 

321. Breech Mechanism Cal. .30— The Sleeve— The Extractor. 

The Sleeve (Fig. 320) serves to connect the firing 
mechanism and the bolt, and carries the safety-lock and the 
extractor. It consists of a single piece of metal, the lower 
parts, a and c, of which are hollow cylinders, and the upper 
part, /, an arm of the shape indicated. The firing-pin and 
•cocking-piece Fk, Figs. 323 and 336, pass through the cylin- 
ders ac, and the slot k, in c, is to allow the hammer to move 
forward and back in firing and cocking. The stud i' enters 
the notch i' , Fig. 319, in the interior of the bolt, and locks 
the bolt and sleeve on the interior. The arm / has a cut, 
d, which embraces- the circular collar d, Fig. 319, on the 
bolt, and locks the sleeve and bolt together on the exterior. 


This locking on the interior and exterior, allows the oolt to 
turn, while the sleeve remains fixed, but does not allow 
longitudinal motion of the bolt without the sleeve. The 
fork e in front carries the extractor E, which is secured in 
it by a screw i. The shoulder g forms a seat for the spiral 
main spring G, Fig. 323, which surrounds the firing-pin 
F. The safety-lock is shown in rear. It consists of a 
thumb-piece, L, and spindle, /. Its object is, first, to lock 
the bolt in the firing position, so that the breech cannot open 
accidentally ; and second, to lock the firing-pin in the full-cock 
position, so that the piece cannot be accidentally discharged. 
Both these operations are performed at the same time, as 
follows : 

The spindle /is half cut away, as explained in the case 
of the magazine cut-off. The thumb-piece L is cut away 
also, so that when turned to the left the cut-away portion 
forms part of the interior surface of the cylinder c, through 
which the cocking-piece can pass freely. When in this posi- 
tion also, the cut-away part of the spindle / forms part of the 
interior surface of the cut d, and the collar d, Fig. 319, on 
the bolt can rotate freely in this cut. When the thumb-piece 
L is turned to the right, the cut-away part no longer forms a 
portion of the interior surface of the cylinder c, and hence the 
cocking-piece cannot enter this cylinder to move forward. 
At the same time, the rounded part of the spindle /, turns 
down into the cut d, and its front end enters the notch /, 
Fig. 319, in the bolt, thus preventing the latter from rotating. 
The rear end of the bolt fits against the shoulder 0, so that 
the exterior of the cylinder c and the exterior of the bolt 
form one continuous surface. 

The cylinder a enters the interior of the bolt. 

The Extractor (Fig. 321) is a long bar, E, having a 
hook, 0, at its extremity which engages over the rim of the 
cartridge. It is attached at the other extremity to the 
sleeve /, as already explained, e is a projection which rests 
against a corresponding shoulder, e, on the guide-rib r, of 
the bolt, Fig. 319. q is a recess fitting against a shoulder, r, 
in the receiver, Fig. 313, in the locked position, and p a 
spring which acts against the lower surface of q on the re- 



ceiver, to force the extractor down over the rim of the car- 
tridge. The extractor has a slight motion around the screw 
i, which is necessary in dismounting the mechanism. 

Fig. 321. 

322. Firing Mechanism — General Principles— Conditions for Good 
Firing Mechanism — Firing Mechanism of Springfield Rifle. 

The ammunition used with all modern- small arms con- 
tains a central primer of mercuric fulminate, which is ignited 
by a blow from the firing mechanism. 

The method generally adopted is to transmit this blow 
through the medium of a firing-pin passing through the 
breech mechanism. The pin may be acted on directly by a 
spring which forces it forward when the trigger is pulled, 
Or it may be acted on by a hammer which is itself acted on 
directly by a spring. The first method is that now generally 
adopted for bolt-guns, the second being used in the Spring- 
field and some older forms of breech-loaders. 

Conditions to be fulfilled by a Good Firing Mech- 
anism. — A good firing mechanism should fulfil the following 
conditions : 

1. It should ignite the primer with certainty and without 
piercing it. 

2. It should not be hard to operate, as this causes loss of 
aim ; nor too easy, as this leads to accidents. 

3. Its parts should be simple, strong, few in number, 
easily dismounted and assembled, and interchangeable. 

4. It should be cocked automatically by the opening or 
closing of the breech. The reasons why cocking on open- 
ing is preferred have been given. 

5. It should have a safety-device to prevent accidental 



discharge when the piece is carried loaded, and should show 
clearly whether it is cocked or not. 

Firing Mechanism of Springfield Rifle. — The prin- 
cipal parts of this mechanism are (Fig. 322) : 

The firing pin F; 

The hammer b ; 

The tumbler c; 

The main spring d; 

The sear e and sear-spring e 1 ; 

The trigger/". 

Fig. 322. 

The firing-pin F passes through the breech-block D, and 
projects to the rear. The hammer b is fastened to the tum- 
bler c by the tumbler-screw, and fits on a square arbor or 
shaft, so that the hammer and tumbler must rotate together. 
The tumbler has three notches: a full-cock, 1 ; half-cock, 2; 
and safety-notch, 3. The main spring d is attached to the 
tumbler by a swivel, d'. The sear e is a pivoted lever, and 
is acted on by the sear-spring /, which forces it against the 
tumbler, and hence it is always ready to catch in one of the 
notches 1, 2, or 3. The trigger / is a pivoted lever, and 
acts against a projection on the long arm of the sear. The 
tumbler and sear are held in place, and supported on the 
inside, by a piece called the bridle, not shown in the figure. 


All the parts except the firing-pin and trigger are assem- 
bled to a flat pla-te, a, called the lock-plate, which is secured 
to the right side of the gun by two screws. 

Action of the Mechanism. — When the trigger / is 
pulled in the direction of the arrow i, the sear is withdrawn 
from its notch in the tumbler, and the action of the main 
spring causes the hammer and tumbler to rotate in the di- 
rection of the arrowy, striking a blow upon the firing-pin, 
which is thus driven forward against the primer, explod- 
ing it. 

323. Firing Mechanism of the Cal. .30. 

The principal parts of this mechanism are (Fig. 323) l 
The firing-pin /''and striker F' ; 
The main spring G ; 
The cocking-piece K; 
The sear H and sear-spring H' ; 
The trigger T. 

Fig. 323. 

The firing-pin is composed of two parts, the body F and 
the striker F', the method of connection of the two being 
indicated in the figure. The striker can thus be readily 
replaced when broken, or removed to permit the replacing 
of a broken main spring. The firing-pin passes through the 
sleeve / and the bolt, as already explained, and the main 
spring G rests between the rear shoulder of the striker F' 


and the front shoulder £• on the sleeve, Fig. 320. It is evident 
that when the firing-pin is drawn back, the main spring will 
be compressed, since the sleeve / is fixed with reference to 
the Din. The cocking-piece K is screwed to the rear end of 
the firing-pin. The part g is roughened to give a firm hold 
to the fingers in cocking. The part k carries the full-cock 
notch i and the wedge-shaped cocking-nose j, all these 
being in one piece. The cocking-nose j engages in the 
notch k, Fig. 319, in the rear end of the bolt. 

The sear H is a piece of metal of the shape shown,, 
hinged at a to the receiver, and its nose c, passing through a 
cut in the bottom of the receiver, engages in the full-cock 
notch i. It is constantly pressed upward into this notch by 
the spiral sear-spring H', one end of which bears against 
the receiver, and the other against the sear. The trigger T 
is pivoted to the sear. At the rear it rests against the 
bottom of the receiver, at the point m, and after the trigger 
is pulled slightly the point n comes into bearing against the 
bottom of the receiver, the point m losing contact. 

Action of Mechanism. — Suppose the piece fired. 
When the bolt is rotated to the left by its operating-handle, 
the inclined side of the notch k, Fig. 319, in the bolt, presses- 
against the corresponding side of j, Fig. 323, and forces the 
cocking-piece, firing-pin, and striker backward, till the end 
of j rests against a notch on the rear end of the bolt. The 
firing-pin is thus drawn back and cocked, the main spring G 
being compressed. 

After the introduction of the cartridge into the receiver, 
the bolt is pushed forward and rotated to the right, to 
lock it. 

In moving forward, the full-cock notch catches against 
the sear H, and the firing-pin is now held back by the sear. 
When the bolt is rotated to the right for locking, the slight 
forward motion completes the compression of the main 
spring, and the rotation brings the nosey" and part k of the 
cocking-piece opposite the notch k, Fig. 319, in the bolt. 
When the trigger is pulled in the direction of the arrow, the 
nose c of the sear is lowered slowly at first out of the full- 
cock notch i. As the pull of the trigger continues, the point 


m loses its bearing against the bottom of the receiver, and 
the point n comes into bearing. The lever-arm being thus 
increased, the nose of the sear at the last moment, moves 
•quickly out of its notch i ; the firing-pin is forced forward 
under the action of the main spring G, and the cartridge is 
zfired. If the bolt is not properly locked, the notch k, Fig. 
319, on the bolt will not be opposite the nose/, Fig. 323, of 
the cocking-piece, and the latter either cannot move for- 
ward sufficiently far to allow the firing-pin to strike the 
primer, or, if the bolt is nearly locked, the forward motion 
of the cocking-piece will cause/ to strike the inclined side 
of the notch k, Fig. 319, and thus cause the bolt to rotate to 
the right, and completely lock it. This is an additional 

324. Sights— General Principles — Position. 

There are two sights for small arms : 

1. An adjustable rear sight- 

2. A fixed front sight. 

Rear Sights. — A good rear sight for a military arm 
should be simple, solid, easy of repair, graduated so that 
the marks can be readily seen, and so arranged that when 
the rear-sight notch is set to any particular graduation it 
will not be displaced by the shock of firing, or by any other 
means, except when changed by the firer. The form of the 
notch should be such as to enable the target to be seen easily. 

It should be out of the way and well protected when not 
in use, to avoid being broken, and it should contain all the 
graduations required up to the extreme effective range of 
the arm. The requisite of simplicity, excludes peep and 
telescope sights, except for selected marksmen, and the flat 
trajectories of the small-calibre rifles have greatly simplified 
the rear sights by reducing their heights, and doing away 
with corrections for wind, and to some extent for drift. 

Elevations are marked in ranges and not in degrees, as 
the ammunition is invariable. 

The rear sight generally consists of a leaf which is 
hinged to a base, the latter being screwed to the barrel of 
the gun. 


The base carries a flat spring which bears against the 
lower edge of the leaf and keeps it upright when in use, or 
folded down against the base when not required. 

The leaf is graduated in ranges (yards) and carries a 
slide which has a notch cut in. it forming the rear-sight 

This slide moves along the leaf, and is clamped at any 
graduation and held firmly in place. 

Front Sight. — The front sight is generally a stud set 
at the muzzle, and terminates in a thin edge parallel to the 
axis of the bore. It should be sufficiently strong, to pre- 
vent injury by the rough usage of service. 

Position. — The front and rear sights are generally 
so placed, that the notch of the rear sight, and top of the 
front sight, shall be in a plane passing through the upper 
element of the barrel and the axis of the bore, and at as 
great a distance apart as possible, so as to give the longest 
sight-radius attainable, consistently with distinct vision of 
the target and the two sights. In some arms, as the Spring- 
field, the rear sight has an arrangement for correcting for 
wind, and the slide is set with an inclination to the left 
equal to the permanent angle of drift. 

325. Sights for Springfield Rifle— Sights for the Cal. .30. 

Sights for Springfield Rifle.— Rear Sight. — The 
principal parts are (Fig. 324) : 

The fixed base A ; 

The movable base and spring B; 

The sight-leaf C; 

The sight-leaf slide D. 
The fixed base A is screwed to the barrel. The movable 
base B carries a flat spring, which bears against the lower 
edge of the sight-leaf C and keeps it vertical or folded 
down. This movable base rotates about the pivot E, and is 
moved by the screw F working in a worm on the end of B. 
The sight-leaf is thus moved to right or left, and corrections 
made for wind. The sight-leaf C carries the graduations, 
and is hinged to the movable base at G. It also carries the 



binding-screw H, which can be made to bear against the 
sight-leaf slide, and thus clamp it in any position. 

The sight-leaf slide D carries the rear-sight notches i, 2 r 
3, 4, and 5. No. 5 is used for ranges up to 200 yards with 
the leaf down. 

Fig. 324. 

For distinction Nos. 1 and 3 will be called peep-sights, 
and Nos. 2 and 4 open sights. 

If the peep-sights 1 and 3 are to be used, No. 1 is em- 
ployed from 200 to 1350 yards, the right-hand arrow on 
No. 1 coinciding with the graduations. 

For 1400 yards the leaf-slide is pushed down, and No. 3 
is used, its mark coinciding with the graduation 14. 

From this to 2000 yards the left-hand arrow on No. i< 
coincides with the left-hand graduations, the sight being 
taken through No. 3. 

If the open sights 2 and 4 are to be used, No. 2 is 
employed from 200 to 1400 yards. The leaf-slide is then 
pushed down, and No. 4 is used, the left-hand arrow on No. 
2 coinciding with the left-hand graduations. The correc 7 
tions for wind are marked on the fixed base, and the leaf- 



slide is set at an inclination to the left equal to the perma- 
nent angle of drift. 

Front Sight. — The front sight, Fig. 324, consists of a thin 
Hade, I, set in a stud. 

Fig. 325. 












Sights for Cal. .30. — Rear Sight. — The principal parts 
are (Fig. 325): 

The fixed base and spring A ; 

The leaf B ; 

The leaf-slide C. 
The fixed base is screwed to the barrel, and carries the 
flat spring which bears against the lower edge of the leaf 
B, and keeps it upright or folded. The leaf B is hinged to 
the base at d and is graduated on both sides, beginning with 
700 yards. From 300 to 600 yards the fixed base is cut in 
steps, and the steps marked as in the figure. For ranges up 
to 600 yards, the leaf is folded down, and the slide C rests 
upon the corresponding step, the sight being taken through 
the notch e. Beyond 600 yards the leaf is upright, the top 
surface of the slide coinciding with the, graduation, and the 
sight is taken through the notch/. The slide C is clamped 
in place by a serrated piece contained in the slide, and acted 
on by a spiral spring which presses it constantly against 
notches on the right-hand inner edge of the leaf. 


A pressure on the button ^releases this catch, and the 
slide may be moved up or down. The arrangement is shown 
in section in the figure. 

The notch e is set slightly to the left of the axis of the 
bore and corrects for drift at 500 yards. For distances less 
than 500 yards this correction is too great, and for those 
greater than 500 yards too small. 

The notch / is similarly set to the left of the axis of the 
bore and corrects for drift at 1000 yards. For distances less 
than this the correction is too great, and for distances 
greater than 1000 yards, too small. The notches on the leaf 
and slide are exactly similar to those on the sight of the 
Springfield rifle. , 

Front Sight. — This is shown at F. It resembles the 
Springfield front sight, and differs from it principally in 
being higher. 

326. The Stock and Mountings. 

The Stock. — The stock is that part of the arm to which 
all the other parts are assembled, and it serves — 

1. To facilitate the handling and pointing, to diminish 
the shock of recoil by distributing it over a greater area at 
the shoulder, and to stiffen and protect the barrel. 

2. In some magazine arms to carry the supply of am- 
munition required for rapid fire, and in all arms to carry 
certain parts necessary for the service, security, or preserva- 
tion of the piece. 

For lightness it is made of wood, and for strength this 
wood should be of close grain, and it should be well sea 
soned to prevent warping ; walnut is generally used. 

It is widened at the butt, a, Fig. 326, to distribute the 

pressure of recoil over the shoulder, and is crooked at the 
small of the stock, b, for convenience of aiming. This crook 


must not be excessive, as it causes rotation about the 
shoulder, with a lever-arm, ac, which increases with the 
crook, and may cause inconvenience. It also weakens the 
stock, since the wood is cut across the grain at this point. 

In some cases, to avoid this weakening and give room 
for the mechanism, the stock is made in two distinct parts, 
called respectively the butt-stock and the tip-stock. With 
smokeless powders, the barrel becomes excessively heated ; 
and to prevent contact with the hand, the upper part of the 
barrel, at the rear, is also covered with wood. 

Under the head of mountings are included the wiping- 
rod, the bands and tip, the butt-plate, trigger-guard, swivels, 
and the various pins and screws by which these parts are 
secured to the gun. 

The wiping-rod is screwed into its seat for a short dis- 
tance, to avoid displacement in firing. 

The bands assemble the barrel to the 
stock, and are not continuous, but split, Fig. 
327, and are assembled by a screw, a. They 
can thus be readily adjusted to the stock 
and barrel, and any undue binding prevented, 
as this might cause vibration in firing. 

The butt-plate and trigger-guard preserve 
the butt and trigger respectively from wear 
and accident, and the swivels are used for Fig. 327. 
stacking and to support the gun-sling. 


327. Advantages of Magazine Arms — Definition — Conditions to be 
fulfilled by a Good Magazine Arm. 

Advantages. — In ordinary breech-loaders three opera- 
tions are necessary to prepare for firing : 

1. Open the breech ; 

2. Insert the cartridge ; 

3. Close the breech. 

The longest of these is the time required to take the 
cartridge from the box or belt and insert it in the gun. 


The rapidity of fire is therefore greatly increased if the 
cartridges can be automatically introduced, and the three 
operations reduced to two, viz., opening and closing the 

As, however, the cartridges so introduced must-be carried 
by the piece in some convenient receptacle, it is evident that 
the number so carried is limited, and hence automatic intro- 
duction of the cartridges cannot be continuous beyond a 
few shots. 

The advantage of a magazine arm is, then, that it can 
furnish a certain number of shots in a very small interval of 
time ; and in order to make use of this advantage it is neces- 
sary to be able to reserve this supply till needed, and ordi- 
narily to use the arm as a single-loader. 

This leads to the conclusion that a good magazine arm 
should be also a good single-loader, and should fire as 
rapidly, when used as such, as any good single-lbader, since 
the arm is used habitually as such, and only in emergencies 
as a magazine gun. 

Definition. — A magazine or repeating arm may then be 
defined as one in. which a certain number of cartridges are 
introduced in succession, automatically and rapidly, into the 

Conditions to be fulfilled by a Good Magazine 
Gun. — A good magazine gun should fulfil the following 
conditions : 

i. When used as a single-loader it should fire as rapidly 
as any ordinary single-loader. 

2. When used as a magazine arm it should give the 
greatest possible rapidity of fire, and the mechanism should 
work well and regularly when rapidly used. 

3. It should allow the change from single-loader to 
magazine fire to be readily and quickly made, and the de- 
vice for making this change should be readily seen, so that 
no mistake can be made ; and so placed that it cannot be 
accidentally operated. 

4. It should afford an easy and rapid method of recharg- 
ing the magazine. 

5. The cartridges in the magazine must not be damaged 



or deformed by firing or by handling the piece, or be liable 
to explode by the shock of discharge. 

6. The weight of the piece with magazine and cartridges 
must not exceed that usually allowed for small arms. 

7. It should afford a ready view of the number of car- 
tridges in the magazine at all times, so that the supply may 
not be exhausted before they are needed. 

328. Classification of Repeating Mechanism. — The Detachable Maga- 
zine — Lee Magazine — Advantages and Disadvantages of De 
tachable Magazines. 

Classification. — The repeating mechanism includes the 
magazine in which the supply of cartridges is carried, and 
the means by which the supply is fed to the receiver. As 
these are generally combined, it is customary to classify the 
mechanisms according to the magazines used. 

Magazines are classified into — 

1. Detachable ; 

2. Fixed. 

Detachable Magazines. — The detachable magazines 
are generally box-shaped, and are placed in rear of the 
barrel and below the receiver. They are called detachable 
because they may be readily detached from the gun. They 

Fig. 328. 

are generally made of thin sheet steel, and contain a spring 
or some device by which the cartridges are constantly 
pressed upward toward the receiver. The top of the 
magazine is folded over for a short distance at the rear, a, 
Fig. 328, and these folds hold the cartridges in place against 



the action of the spring. When the bolt is drawn to the 
rear over the cartridge, a portion, b, of its rim projects be- 
yond the folds. As the bolt is pushed forward, it strikes 
the rim b and pushes the cartridge forward beyond the folds, 
out of the magazine and into the receiver and chamber. 
This device in some similar form is found in all box maga- 

Lee Magazine. — The Lee magazine is a good example 
of this system, and is shown in Fig. 329 with its method of 
attachment to the gun. 

Fig. 329. 

a is the magazine, b a projection on its rear end, c the 
magazine-catch operated by the U-shaped sear-spring d, e a 
folded spring which pushes the cartridges upward. The 
filled magazine, containing five cartridges, is inserted from 
below, in a cut made for it in the stock and receiver, and 
pushed upward till the magazine-catch c snaps under the 
projection b. When the magazine is empty it is released by 
pressing on the magazine-catch c, and withdrawn. 

Advantages. — These are : 

1. Since they can be used only when fixed in place, it is 
always evident whether or not the magazine supply is being 
employed. This does not, however, apply to those which 
are lowered vertically to cut off the supply. 

2. A number of these can be carried loaded, and as they 


can be inserted quickly, the rapid fire can be kept up con 
tinuously for some time. 

Disadvantages. — i. The magazine has considerable 
weight and adds to the burden carried by the soldier. This 
additional weight could otherwise be utilized to increase 
the number of cartridges carried. 

2. The magazines are apt to be thrown away or lost 
when empty, and when lost the gun cannot be used as a 
magazine arm. 

3. The cut through the bottom of the receiver is incon- 
venient when the gun is used as a single-loader, and when 
the magazine is attached it must generally be used ; that is, 
the gun cannot be used with facility as a single-loader. 

To remedy the inconvenience of the cut in the receiver, 
the Lee gun has a spring slide which closes this cut as soon 
as the magazine is withdrawn, and the insertion of the 
magazine pushes this slide out of the way. In some guns 
of this type a cut-off is arranged by which the magazine is 
lowered vertically, so that the cartridges will be out of the 
way of the bolt when the gun is to be used as a single- 

329. Fixed Magazines — Classification — Description of the Jarmann 

Classification. — Fixed magazines may be classified 
according to their shape into — 

1. Tubular; 

2. Box. 

Tubular magazines may be placed either under and 
parallel to the barrel, in the front part of the stock ; or in 
the butt, in rear of the barrel. 

Box magazines are placed in rear of the barrel, and 
directly in front of the trigger-guard. 

Tubular Magazine under Barrel — Jarmann Maga- 
zine. — The Jarmann magazine-gun, formerly used in Nor- 
way, may be taken as an example of the tubular magazine un- 
der the barrel. In Fig. 330, a is the barrel ; b the magazine ; c 
the spiral spring which forces the cartridges to the rear ; d 
the piston attached to the end of the spring ; e the carrier 



which lifts the cartridges from the mouth of the magazine 
to the receiver ; / the carrier-spring, which is fork-shaped 
and rests on two pins,^, pressing the carrier down ; h the pin 
by which the carrier is attached to the receiver, and around 

v ra 


Fig. 330. 

which it rotates ; * a shoulder on the rear end of the carrier, 
projecting above the bottom of the receiver when the carrier 
is down ; / a corresponding shoulder and recess on the lower 
side of the front of the bolt, which, as the bolt is drawn back 
allows the carrier first to drop under the action of the spring 
•/, and immediately afterward, as the bolt moves further 
back, strikes against i and raises the carrier ; k is a projec- 
tion from the lower front end of the carrier, whose object is 
to work the cartridge-stop and hold back the next cartridge 
in the magazine. This projection k, carries a pin, /, which 
works the cartridge-stop. 

Action of Mechanism. — Suppose the piece fired. The 
breech is then closed by the bolt, the carrier e is held up in 
the position shown in the lower figure by the bearing of the 
lug i on the bottom of the bolt. The carrier thus forms a 
part of the bottom of the receiver.. The cartridges are held 
back in the magazine against the action of the, spring c, by 
the projection k of the carrier, bearing on the head of the 
rear cartridge. 


As the bolt is withdrawn, the carrier e remains in the 
position just described, because its lug i bears continually 
against the bottom of the bolt. When the bolt, in its back- 
ward motion, reaches a position such that the cut/ comes 
over the lug i of the carrier, the latter is free to rotate, and 
moves downward under the action of its spring/. During 
its downward motion the cartridges are kept in place by 
the bearing of the front of the carrier e against the head of 
the rear cartridge. At the last moment of the rotation of 
the carrier, when it occupies the position shown in the 
upper figure, this bearing is removed, and the rear cartridge 
is forced by the spring c, but of the magazine, and on the 
carrier. As soon as this is done, the downward rotation of 
the carrier being completed, the pin /, on the projection k, 
strikes the cartridge-stop m, and causes it to rise and partly 
close the mouth of the magazine, thus preventing the other 
cartridges from being forced out. All this occurs while the 
cut/ in the bolt is over the lug i of the carrier. As the bolt 
is pulled backward still further, the shoulder of/ strikes the 
shoulder of i and raises the carrier e with its cartridge 
quickly to the mouth of the chamber. The bolt is then 
pushed forward and the cartridge inserted. It will be re- 
membered that at this time the cartridges are held back in 
the magazine by the cartridge-stop. To release this stop, 
the bolt, in moving forward, strikes the long lever n of the 
cartridge-stop, which is situated on the right-hand side of 
the receiver. This pushes the lever n forward, lowers the 
stop, and frees the mouth of the magazine, and under the 
action of the spiral spring c, the cartridges move forward till 
the head of the rear one comes into bearing against the pro- 
jection k, which is now in the position shown in the lower 
figure, the bolt being closed. 

The principles explained here are found in modified 
forms in all magazines of this type. The magazine has a 
cut-oft by which the carrier is locked in its upward position 
and the gun may then be used as a single-loader. 


330. Objections to Tubular Magazines under the Barrel — Advan- 


Objections. — The objections to tubular magazines under 
the barrel are : 

i. The cartridges lie with the primer of one against the 
bullet of the next, and hence the shock of discharge is liable 
to explode the primer, or to upset and deform the point of 
the bullet. With modern smokeless powders, although the 
bullet is not so liable to be deformed, owing to its harder 
jacket, it is more liable to be driven down into its case, 
since any excessive crimping of the bullet to the case, which 
would tend to prevent this, increases the pressure in the 
gun, by increasing the resistance to motion at the origin. 
If the bullet be forced down into the case, the density of load- 
ing of the charge is increased, and hence also the pressure. 

2. The spiral spring which forces the cartridges into the 
carreer, must be long, as it has to act over a great distance. 
Hence it is tightly compressed at first, and its actipn be- 
comes very slight on the last cartridge, and is therefore 

3. When the magazine is full, the centre of gravity of 
the system is carried forward, and as it is emptied this cen- 
tre changes. 

4. The weight of the arm increases considerably when 
the magazine is loaded. 

5. The magazine is difficult to load, as the cartridges must 
generally be inserted singly. 

6. The state of supply of the magazine cannot be seen. 

7. Unless the bolt is drawn back to its full extent, and 
quickly, the carrier will not work properly. 

8. As the magazine-tube is thin, a slight damage to the 
stock may close up the tube so that it will not feed. 

Its greatest advantage is the number of cartridges car- 

331. Tubular Magazine in Butt — Fixed -box Magazines — The 

Mannlieher Magazine. 

Tubular Magazine in Butt.— This was the earliest 
form of magazine, as seen in the Spencer rifle, which was 



used during the Civil War. It has been abandoned, however, 
because it has nearly all the disadvantages belonging to the 
tubular magazine under the stock, and in addition it 
weakens the small of the stock and does not carry a large 
number of cartridges. The Hotchkiss is probably the best 
example of this type. 

Fixed-box Magazine. — This type of magazine has been 
adopted by many of the foreign powers and by the United 

The Mannlicher Magazine. — The Mannlicher maga- 
zine may be taken as a type of this system used abroad. 

Fig. 331. 

In Fig. 331, a is the fixed box, having the bottom open 
at b. This box is fixed in rear of the barrel and in front of 
the trigger-guard, and projects below the stock as in the 
Lee magazine, c is the carrier-lever ; d the magazine-spring, 
which pushes the carrier-lever upward against the car- 
tridges. The cartridges are carried in a packet, e, made of 
tin, the top and bottom edges being slightly folded over, as 
shown in Fig. 328. 

This packet carries five cartridges, and is inserted with 
its cartridges, from above, through the cut in the bottom of 
the receiver, into the magazine a. It is held in place in the 
magazine, by the upward pressure of the carrier-lever c on 


the cartridges, which is transmitted to the packet e by the 
folded edges, and as this would push the packet out of the 
magazine, the catch /, acted on by the spiral-spring h T 
engages against a lug, g, on the rear end of the packet, and 
prevents it from rising. 

Action of the Magazine. — When the filled packet e 
is introduced into the magazine, it compresses the magazine- 
spring d. The packet is pushed down till the catch /snaps 
over the lug g. The cartridges being constantly pressed 
upward by c and d, when the bolt is pushed forward it 
strikes the exposed part of the base of the upper cartridge, 
and pushes it forward beyond the folded edges of the case, 
the surface^' of the receiver guiding the point of the bullet 
upward and into the chamber. When all the cartridges are 
exhausted, the carrier-lever c and spring d no longer exert 
an upward pressure on the packet, and hence the latter falls 
through the opening b in the bottom of the receiver, and 
thus indicates that the supply is exhausted. 

The packet may be removed at any time by pressing on 
the projection i of the catch. 

To cut off the supply the packet must be removed. 

332. Advantages and Disadvantages of the Fixed-box Magazine, 
Mannlicher Type — General Principles of the Cal. .30 

Advantages. — The Advantages of the fixed-box maga- 
zine, Mannlicher type, are : 

i. In common with all box magazines, the cartridges lie 
so that the spring which moves them acts in the direction 
of their least dimension, and therefore the great length and 
irregularity of its action, as in the tubular magazine, are 

2. The cartridges are not liable to explode, or to be de- 
formed in handling and firing. 

3. The centre of gravity of the system is not changed. 

4. The magazine is easily charged. 

5. The packets are light, and hence do not add. much 
useless weight to the soldier's burden, and they are cheap 
and may be thrown away. 


6. The exhaustion of the magazine is automatically 

7. The magazine cannot be lost, and is not liable to 

Disadvantages. — The objections are : 

1. When the packet is in place the arm cannot be used 
as a single-loader without great care ; and when the packet 
is withdrawn the bottom of the receiver is not solid, which 
is an inconvenience. 

2. The cartridges must be carried in packets, and cannot 
be placed in the magazine without them. The packet there- 
fore becomes a necessary part of the mechanism, just as the 
magazine in the Lee gun. 

General Principles of the Cal. .30 Magazine. — The 
magazine of the cal. .30 remedies the last two defects. 

In this gun the magazine is a fixed box, but, instead of 
projecting vertically below the receiver, it is partly hori- 
zontal and partly inclined at the left side, where it opens 
into the receiver. This gives a solid bottom to the receiver, 
so that no inconvenience results from using the gun as a 
single-loader, and the cartridges may be inserted into the 
magazine either singly by hand or quickly from a packet 
carrying five cartridges. This latter arrangement is called 
a quick-loader, and is used in many other box-magazine guns, 
in which the packet does not form an essential part of the 
mechanism, as with the Lee, and the Lee-Speed or English 

333. Description of the Magazine for the Cal. .30. 

This magazine is situated under the receiver, in front of 
the trigger-guard and in rear of the barrel. It consists, 
Figs. 332 and 333, of the horizontal part m (see also Fig. 313) 
and the curved part O. 

The horizontal part is in one piece with the receiver, 
and the curved part is formed by the separate piece O, of 
the proper shape, secured to the left side of the receiver. 

The opening z', through which the cartridges pass to the 
receiver, is narrowed at the rear (see Fig. 313) correspond- 
ing to the folding down of the sides of the magazines in the 



Lee and Mannlicher, and for the same purpose — that is, to 
hold the cartridges in the magazine, against the action of 

Fig. 332. 

the carrier-lever and spring ; and as with other box- 
magazines, the cartridge must be pushed forward by the 
bolt, beyond this narrow part, before it can rise into the 
receiver. The bottom of the receiver at z is left solid, with 
the advantages noted. 

Fig. 335. 

The cartridges are pushed to the left, and into the re- 
ceiver, by the carrier-lever N, Figs. 334 and 335. This lever 
has a spindle, a, and lug, e, at its forward end and below, 
against which rests a flat bow-spring, 5. This spring S is 
carried in a small recess, r, below the receiver (see also Figs. 
332 and 333). The rear end of .Shears against the side of 
this recess, r, the front end against the lug e on the carrier- 
lever, and against the back of the spring rests the lower 
edge, s, of the gate M which opens and closes the mouth of 
the magazine. 

The spring 5 is thus under constant compression, due to 
the action of the gate, and it forces the carrier-lever to the 



left in the magazine. When the gate is opened, as in Fig. 
332, a lug, n, attached to it, Figs. 334, 335, presses against the 
carrier-lever and forces it to the right against the action of 
the spring S, thus leaving the magazine clear for loading. 
The spring 5 acts also to keep the gate M open or closed, 
just as the flat spring on the rear sight keeps the sight-leaf 
up or down. 

The gate M, Fig. 334, has a thumb-piece, t, by which it is 
opened and closed, and it is assembled to the side of the 
receiver by the pin P, Figs. 332 and 333. The cut-off is 
shown at c, same figure. 

Action of Mechanism. — To fill the magazine the gate 
M is opened by the thumb-piece /, and the five cartridges 
inserted by hand singly, or all at once from a quick-loader, 
the carrier-lever N being held back as explained. 

When the gate is closed the carrier-lever comes into 
action, and forces the cartridges to the left and upward. 
The first four cartridges, by their shape, act to push each 
other upward as soon - as they reach the curved part of the 
receiver. The fifth cartridge is pushed upward by the 
shape of the upper side of the follower-lever. If the cut-off 

Fig. 336. 

c is used, it projects as explained into the opening z' of the 
magazine, Fig. 333, and forces the upper cartridge down 
sufficiently far to be out of the way of the bolt. 

The assembled mechanism of the cal. .30 rifle is shown in 
the firing position in Fig. 336. 


334. Revolvers — Classification — Conditions to be fulfilled by a Good. 
Service Revolver — Remarks. 

Classification. — The revolver is a weapon for personal, 
defence at short distances, not exceeding 50 or 60 yards, and 
is employed principally by mounted troops and by officers. 

They are divided into three classes : 

1. Single-action revolvers, or those which must be cocked 
by hand before each fire. 

2. Self-cocking revolvers, in which by pulling the trigger 
the cocking and firing are accomplished, till all the chambers 
are emptied. 

3. Double-action revolvers, which act as single-action or 
as self-cocking at the will of the firer. 

Conditions to be fulfilled by a Good Service 
Revolver. — 1. Its mechanism should be simple, strong, 
easy to dismount and assemble, and interchangeable. 

2. Each chamber which is to be fired should stop exactly 
in the prolongation of the barrel. 

3. The mechanism should work well whether the revol- 
ver be fired rapidly or slowly ; this rapid or slow fire being 
readily employed at will. 

4. The bullet should possess sufficient energy to stop a 
man at 50 or 60 yards. 

5. It should be easy to load, and the empty cases should 
be readily extracted. 

Remarks. — The principal points with reference to the 
working of a revolver are, to insure the stoppage of rota- 
tion of the cylinder in the proper position, to obtain rapidity 
of fire when needed and slow fire at other times, and to be 
able to load and extract easily. 

The stoppage of rotation of the cylinder at the proper 
time* has been successfully accomplished. The rapid and 
slow firing at will requires a revolver of the third class, or 
a double-action revolver. The single-action revolver gives 
the slow fire, but will not fire rapidly, while the self-cocking 
revolver, although giving a rapid fire, does not give an ac- 
curate slow fire, because of the prolonged pull upon the 
trigger, which is apt to derange the aim. The loading and 
extraction are readily accomplished in the service revolver, 


all the empty cases being ejected automatically at the same 
instant, and the chambers can be loaded from a quick-loader. 
The condition of certainly stopping a man at 50 yards has 
caused the retention of larger calibres for the revolver than 
for the rifle, those of the revolver being 0.38 and 0.45 inch. 
The revolvers adopted for the U. S. service are the Colt's 
double-action cal. .38 and the cal. .45. The mechanism of the 
revolver is best explained from a model. 


335. History — Advantages and Disadvantages of Metallic Car- 
tridge-cases — Folded-head Cartridges. 

History. — Small arms were originally loaded by pour- 
ing in the powder and then inserting the ball, each of these 
being carried separately and loose. 

The powder-charge was next wrapped in paper, and 
hence the name cartridges, from charta, paper ; later the 
powder and ball were united in one package, and the opera- 
tion of loading was preceded by the tearing open of the 
paper containing the powder, pouring it into the ban-el, 
and then inserting the ball. These arrangements were used 
with muzzle-loaders, and continued up to the Civil War. 

With the introduction of breech-loaders, a change in the 
•cartridge became necessary. The gas from the powder 
•escaped through the opening of the breech, occasioning 
loss of force, and it also clogged the firing mechanism. 

To obviate the defect of the escape of gas through the 
opening of the breech, various devices were provided, such 
as the De Bange pad in the French Chassepot rifle, a rubber 
packing-ring, etc. These devices prevented the escape in 
the direction indicated as long as they were uninjured by 
the gas, but did not prevent it from penetrating into the 
firing mechanism, which was soon clogged. 

To avoid the expense of manufacture, and the increase of 
weight, which the use of the metallic case entailed, and also 
to avoid the difficulties of extraction, combustible cartridge- 
cases were used with the early breech-loaders. 


But the objections already stated caused them to be 
abandoned and led to the adoption of the metallic case. 

Advantages and Disadvantages of the Metallic 
Case. — The metallic case presents the following advan- 
tages : the escape of gas is entirely prevented ; the powder 
is well protected against shock and moisture ; the compo 
nents of the cartridge — powder, primer, and bullet — are 
complete and invariable ; the dimensions of the cartridge- 
case are exact, and there is no difficulty in loading. 

The disadvantages are, the increase of weight of the 
cartridge and the expense of fabrication. The first is. 
greatly reduced by the use of smokeless powder and the 
reduction of calibre, and the second by improved processes, 
of manufacture, by which all the parts are rapidly and 
cheaply made by machinery. 

Folded-head Cartridges. — The earliest metallic car- 
tridges were made of copper, with a folded head (Fig. 337), 
the fulminate by which the charge 
was fired being contained in the 
fold a. 

These are called rim - fire car- 
tridges. The objections to them are : 
1. The fulminate is exposed to< 

shocks, which may cause accidental 
Fig. 337. ,. , . , ,,. 

discharge in handling. 

2. The charge of fulminate is larger than necessary to 
produce discharge, and hence tends to rupture the head of 
the shell at the fold. 

3. The fulminate is not evenly distributed ; and as the 
firing was produced by a blow of the hammer on the rim, 
if this blow fell where there was no composition a miss-fire 
would result. 

4. The head of the case is not supported by the walls of 
the chamber b at the fold, and hence, due to this cause and 
to the excess of fulminate, the head was liable to shear off. 

The principal advantage is that, as it was generally used 
in arms with tubular magazines, there was little danger of 
explosion by the shock of firing, since the point of the bullet 
did not rest against the primer in the magazine. 



Fig. 338. 

336. Folded-head Cup-anvil Cartridge— Solid-head Cartridge. 

Folded-head Cup-anvil Cartridge.— To remedy the 
shearing of the head of the cartridge, due to non-support 
by the walls of the chamber, and 
also the defects of the rim fire, the 
folded-head cup-anvil cartridge, with 
the fulminate at the centre of the 
head, was devised. Cartridges with 
central primers are called centre-fire 

This cartridge is shown in Fig. 
338. In order to prevent the action 
of the gas upon the fold a, a gas- 
check cup b was inserted in the head 
of the case. When the gas ex- 
panded, its pressure was exerted 
upon the cup., and the fold a protected. 

In the rim-fire cartridge, the blow of the hammer upon 
the fold of the head was resisted by the wall of the chamber, 
which thus prevented the fold from yielding, and the effect 
of the blow was transmitted to the fulminate. In this case 
the wall of the chamber acted as an anvil. 

When the fulminate was placed at the centre of the head 
it was necessary to provide an anvil as before, to resist the 
blow of the firing-pin, and this anvil was furnished by the 
cup, b. As this cup performed both functions, as above ex- 
plained, it was called a cup anvil. The anvil is a common 
feature of all primers, and is necessary for the reason stated. 

The cup anvil was held in place by two crimps, c, in the 
case. The fulminate is at d, and ee are the two vents through 
the cup anvil, by which the flame from the fulminate escapes 
to the charge, the fulminate being fired by the blow from 
the firing-pin^ 

The copper of which the folded-head cup-anvil cartridge 
is made is objectionable, as it is too soft, and the extractor 
frequently cuts through it and fails to withdraw the case, 
and also, owing to its lack of elasticity, it is apt to stick in 
the chamber after firing. For these reasons brass is prefer- 



able, as it is harder and more elastic, but owing to its 
hardness the head cannot be folded. 

Solid-head Cartridges. — For these and other reasons 
the folded-head cup-anvil cartridge of copper was aban- 
doned, and the solid - head brass 
cartridge adopted in its place. 

In this cartridge (Fig. 339) the 
head is formed by pressure, causing 
the metal to flow into the shape 

The danger of shearing at the 
head is avoided, since the bottom of 
the case, a, inside, is in front of the 
shearing plane, b. 

The primer is inserted from the 
outside in a pocket, c, in the base of 
the cartridge, and consists of the 
cup d, the fulminate e, and the anvil f. The anvil is made 
of copper, and has a cut, g, across the bottom, and two ver- 
tical holes, h, at the sides, communicating with g, through 
which the flame from the fulminate passes to the charge by 
the vent 2 in the primer pocket. 

The principal defect of this cartridge is that its walls are 
thinner in front than in rear, and when the cartridge is 
fired the front part expands more than that in rear, and is 
liable to stick. Hence if there is any movement of the case to 
the rear, it is apt to tear apart. 

Fig. 339. 

337. Components of the Cartridge — The Bullet — The Powder. 

The Bullet. — For the older arms the bullet was made 
of pure lead cast in a mold. As improvements were made, 
the soft lead was found to shear in the grooves and cause 
" leading." 

Hence the lead was hardened by alloying it with some 
other metal, such as tin or antimony. The Springfield bullet 
is an alloy of lead and tin. With the introduction of small 
calibres, high velocities, and rapid twist, the hardened lead 
did not present sufficient resistance to shearing, and the 



jacketed bullet was adopted. The jacket at present used is 
cupro-nickelled steel. 

The casting of the bullet also was objectionable, since the 
density was not uniform, and the centre of gravity fre- 
quently did not coincide with the longer axis, giving rise to 
irregularity in flight. For this reason the bullet was formed 
by compression between dies, and more uniform density 
thus obtained. In the Springfield bullet (Fig. 340) three 
grooves or cannelures are formed at the rear end, and these 
are filled with vegetable wax for lubrication of the bore. 
With the cal. .30 bullet (Fig. 341) it is found that these are 
not necessary, and they have been abandoned. 

The shape of the bullet is cylindro-ogival for the Spring- 
field and cal. .30. The two bullets are shown (Figs. 340 and 
341). The weights are: Springfield, 500 grains; cal. .30,220 

Fig. 340. 

Fig. 341. 

Fig. 342. 

Recent experiments have been made with a tubular steel 
"bullet, the Krnka-Hebler. 

This bullet (Fig. 342) is made entirely of steel except the 
narrow copper rotating band, a, around the middle. On 


the rear end is a sabot, b, made of vulcanized fibre and 
weighing only a few grains ; its object being to receive the 
pressure of the powder-gas over a greater extent of surface, 
and to act as a gas-check, preventing the escape of gas 
along the sides of the projectile. When the projectile leaves 
the bore, the pressure of the air upon the front surface of 
the sabot causes it to drop off. The central hole allows the 
air to pass through freely in flight, and thus diminishes the 
retardation owing to the decreased surface presented. An 
initial velocity of 3000 ft.-secs. has been obtained with this 
projectile, with a pressure of 46,000 lbs. per square inch in 
the gun. 

The Powder. — Small-arms powder is used in the 
Springfield rifle, weight 70 . grains. It is measured auto- 
matically in a loading-machine, and after insertion in the 
case is slightly compressed before the bullet is put in. The 
charge of smokeless powder varies from 32 to 43 grains, 37 
of Wetteren or 43 of Peyton powder being at present used. 
As it is important with smokeless powders to secure the 
same amount for each charge in order to regulate the 
pressure, these charges are weighed, and to insure greater 
regularity the powder is sieved before loading. 

338. Components of the Cartridge — The Case — The Primer. 

The Case. — The general features of the cartridge-case 
have already been described. The rim is for the purpose 
of extraction, limits the forward motion of the cartridge in 
loading, and fixes its position in the 
chamber. In certain box magazines 
the rim occasions some difficulty if 
care is not exercised in placing the 
cartridge in the magazine. For ex- 
Fig. 343." ample, in Fig. 343, if the cartridges 

occupy the position there shown, it 
is evident that the top cartridge is held by the rim of the 
one next below, and consequently the bolt cannot without 
difficulty push it out of the magazine. To remedy this it 
has been proposed to make rimless cartridges, as in Fig. 344, 
the notch a being for the purpose of extraction. The ob- 



d— i 

jections to these cartridges are that their position in the 
chamber is regulated by the bearing of the shoulder b against 
a corresponding shoulder in the forward part of the cham- 
ber, and as it is impossible to make the length cd exactly 
the same for all cartridges and all chambers, 
short cartridge will have too much play, 
and the head of the case, moving to the rear 
on firing, while the front sticks in the cham- 
ber, for the reasons already explained, will 
cause rupture of the case and fouling of the 
mechanism. In addition, the operation of 
the extractor is not always certain. 

The case of the cal. .30 cartridge is made 
bottle-shaped to reduce its length as much as 
possible in order to give a longer path for 
the gas to work over and to diminish wave 
action, and the exterior is conical to facilitate 
,— x extraction in both 
the Springfield 
and the cal. .30. 

The contact of 
the old nitrate 
powders with the 
brass case caused 




Fig. 344. 
deterioration of the latter, and it 
was tinned to prevent this. 

The effect of the new smoke- 
less powders on the case is not 
known, but the cases are tinned 
as with the old powders. 

The Primer. — Its composi- 
tion has already been explained. 
With the new smokeless pow- 
ders some difficulty has occurred 
in igniting the charge, and the 
strength of the primer has been 
increased, with successful results 
as regards ignition. The primer is, for safety, sunken be- 
low the level of the head of the cartridge. The old Spring- 

Fro- 345- 

Fig. 346. 


field cartridge can be reloaded ; the new smokeless-powder 
cartridge cannot be, except at the arsenals, on account of the 
danger from excessive crimping, and the high pressures 
that result from an error in weight of charge, or from in- 
serting the bullet too far into the case, and also because of 
difficulty in providing reloading-tools for the small calibre. 

The complete cartridges for the Springfield and the cal. 
.30 rifles are shown in Figs. 345 and 346. 




339. Definition — Object — Advantages — Disadvantages — Require- 
ments — Kinds of Machine Guns 

Definition. — A machine gun is one that is loaded and 
fired by machinery. 

Object. — Its object is to deliver a rapid and continuous 
fire, and thereby enable a few men to produce the same 
effect as a larger number armed with the ordinary rifle. 

Advantages. — Owing to the great volume of fire deliv- 
ered by them, they may be employed at decisive moments of 
the attack, and to defend defiles, ditches of permanent works, 
and for their moral effect against mobs and in street-fight- 
ing. In the Naval Service they are mounted in the tops, to 
sweep the enemy's decks, drive the cannoneers from their 
guns, and to repel boarders. 

Disadvantages.— These guns are mounted on wheeled 
carriages, and transported like artillery. They therefore 
appear naturally to belong to that arm of the service. But 
as they generally fire small-arm ammunition, they are unable 
to cope with field-artillery at the fighting range of the latter. 

This limits the use of machine guns in the attack to the 
infantry arm, and it is generally considered that for pur- 
poses of attack they are inferior to infantry, as they do not 
possess its mobility. 

For defence the guns are very useful in holding positions 
where they may be permanently mounted, and fired in a 
fixed direction. 

Requirements. — In order that a machine gun may fulfil 
its functions, it should, when once pointed in a given direc- 



tion, retain that direction unchanged by the shock of firing; 
which requires that there shall be no recoil, and that the 
mechanical operations of loading and firing shall not inter- 
fere with the aim or working of the gun. These conditions 
are very difficult to fulfil, and are perhaps more nearly at- 
tained in the Maxim automatic gun than in any other. The 
gun must also be capable of being rapidly directed upon 
any particular object, and of having this direction quickly 
changed. This is accomplished in most of them by mount- 
ing the gun on a fork placed upon the carriage, by which 
means a quick motion in azimuth, and also around the axis 
of the trunnions, can be given. 

The gun must be managed by a small number of men, 
who should be well protected by shields from the enemy's 
fire. The ammunition should in general be the same as that 
used by the infantry, to avoid complication, and a large 
supply must be carried by the gun in a condition ready for 
feeding, in order to insure rapid and continuous fire. The 
mechanism should not be liable to jam or get out of order 
when the gun is fired rapidly ; it should be simple and' easily 
repaired, and the gun should not become heated to such an 
extent as to interfere with firing. 

Kinds of Machine Guns.— The principal machine guns 
which have been tried in the United States are 

The Gatling ; 

The Gardner; 

The Maxim; 

The Hotchkiss revolving cannon. 
Of these, the Gatling and Hotchkiss revolving cannon have 
been adopted for service. 

340. The Gatling Gun — Parts — Barrels — Cylinders— Casing. 

Parts.— The gun consists, Fig. 347, of a number of breech- 
loading rifled barrels, B, usually ten, placed around and par- 
allel to a central shaft, 5. These barrels are held in place 
by two barrel-plates, P, P' , called respectively the front and 
rear barrel-plates. The barrel-plates are circular disks as- 
sembled to the central shaft S, and having holes in them 



through which the barrels pass. The barrels and central 
shaft thus form a cylinder, of which the barrels are the ele- 
ments and the central shaft the axis. 

In rear of the barrels is the carrier-block C, which is a 
metal cylinder attached to the central shaft 5. On the sur- 
face of this cylinder are grooves forming extensions of the 
barrels. These grooves receive the cartridges from the 

feed, and guide them while they are being pushed into the 
barrels by the bolts* and they also guide the empty shells 
while they are being withdrawn from the barrels after firing. 

The outer edges of these grooves have projections which 
act to feed the cartridges, as will be explained. 

In rear of the carrier-block is the lock-cylinder L, a 
second metal cylinder attached to the central shaft S, the 
surface of which forms guides in which slide backward and 
forward, the bolts by which the breech is opened and closed, 
and the cartridges fired. 

On the rear end of the central shaft is a worm-gear, G, 
in which works a worm, W, on the transverse crank-shaft S' . 
By attaching the crank K directly to the rear end of the 
central shaft S, a rapid fire is obtained ; when attached as 
shown, the fire is comparatively slow. 

Casing. — The central shaft, with barrels and mechanism, 
is mounted in a frame, the mechanism being covered by a 
bronze casing which protects it from dust. The shaft S is 
journalled in this frame and casing in front and rear, so that 
the shaft, barrels, carrier-block, and lock-cylinder revolve 
independently of them. 



The trunnions are attached to the exterior of the frame, 
and the gun is mounted on a fork attached to the carriage. 

The fork has a motion in azimuth, and hence the direc- 
tion may be quickly changed without moving the carriage 
as before explained. 

341. The Gatling Gun— Parts— The Bolts— The Cam-groove— Ac- 
tion of Mechanism. 

Fig. 348. 

The Bolts. — There is one bolt for each barrel. Each 
bolt consists, Fig. 348, of a hollow cylinder, through which 
passes the firing-pin a, surrounded by its spiral main spring, 
b. The firing-pin terminates in rear in a head, b' , which is 
used in cocking and firing. Each bolt has a lug, c, project- 
ing from its rear end. This lug fits into a groove in the 
casing, and is the means by which the forward and back- 
ward motion is communicated to the bolts during the rota- 
tion of the barrels. Each bolt acts with reference to its own 
barrel, like the bolt in the cal. .30 rifle, opening, closing, and 
locking the breech. The extractor, d, engages over the 
rim of the cartridge before firing, and by the backward 
motion of the bolt extracts the empty case from its barrel. 
e is the guide-rib which fits in a corresponding groove in 
the lock-cylinder, and guides the bolt in its forward-and- 
back motion. 

The Cam-groove. — The rear part of the cylindrical 
bronze casing surrounding the lock-cylinder contains a. 
groove, called the cam-groove, which may be regarded as 
formed by the intersection of the interior of the cylindrical 
casing by a plane, cd, oblique to the axis, as in Fig. 349. 

This gives an ellipse, the upper and lower ends of which,. 




at c and d, are cut off by two planes perpendicular to the 
axis of the cylinder. Hence c c a 

the sides cd of the groove 
are arcs of an ellipse, and the 
ends a and b, arcs of circles, 
with their planes perpendic- 
ular to the axis of the cylin- 
der. The arc b is at a dis- FlG - 349- 
tance in rear of the barrels equal to the length of a bolt, 
and the arc a at a distance equal to the length of the bolt 
plus that of the cartridge, with a small allowance for play 

Action of the Mechanism.— When the crank K, Fig. 
347, is rotated, it causes the central shaft, with the barrels, 
carrier-block, and lock-cylinder, to rotate in the casing. 

The bolts, being held by the guides in the surface of the 
lock-cylinder, also rotate with the barrels and other parts. 
But by the bearing of the lugs c, Fig. 348, of the bolts, in 
the elliptical groove cd,.F'\g. 349, in the breech-casing, the 
bolts on the right-hand side are forced to move forward 
toward the barrels, and those on the left to move back- 
ward. , 

Fig. 350 shows a development of the cam-groove, barrels, 
and firing mechanism; cd being the development of the 
right-hand side of the elliptical groove cd, Fig. 349, and c'd r 
that of the left-hand side of the same groove, while cc' and 
dd' are the developments of the circular arcs b and a, Fig. 
349, respectively. 

When the lugs' c of the bolts, Fig. 348, in this rotation, 
reach the part dd' , called the " loading flat," the cartridges 
drop from the feed into the grooves in the carrier-block, in 
front of the bolts ; as the rotation continues, each right- 
hand bolt is forced forward by the inclined groove cd, 
pushing its cartridge into the barrel. When the cartridge 
is completely inserted, the lug c of its bolt has reached the 
part cc' , called the " firing-flat," and the bolt thus closes the 
barrel, just as the bolt of the cal. .30 rifle. 

While the bolts are thus moving forward, a groove R on 
the right-hand side of the casing, catches the head of the 



firing-pin and retains it, thus compressing the spiral main 
spring and cocking the firing pin. 

This groove R is called the cocking-rib, and is essentially 
a short arc of a circle whose plane is parallel to those of cc' 
and dd'. This arc ends abruptly, so that when the firing-pin 

Fig. 350. 

is cocked and the barrel closed, as in the figure, a continua- 
tion of the rotation causes the head of the firing-pin to 
pass out of the cocking-rib. The firing-pin then moves for- 
ward under the action of the spiral main spring and fires 
the cartridge. The rotation still continuing, the bolts are 
withdrawn by the left-hand groove c'd' ', and as they move 
back, the empty cases are drawn out by the extractors on 
the bolts. 

342. The Gatling Gun — Feeds— Tin Feed-case — Objections — Bruce 
Feed — Objections. 

FEED. — The feed is the method of supplying the car- 




tridges to the gun. Various feeds have been used with the 
Gatling gun, and changes have been made in them to cor- 
rect defects as they developed. 

Tin Feed-case. — The first feed consisted of a tin case, 

A, Fig. 351, of trapezoidal cross-section, con- , 

taining 40 cartridges. 

The cartridges were placed horizontally 
in this case, lying one above the other, and 
were held in the case by a spring, s, at the 
lower end, the upper end being closed. 

A weight, w, at the upper end rested 
on the column of cartridges, and was provided 
with a projecting thumb-piece, t, the whole 
sliding along the case in a groove, g, cut in the 
side. When in use, the lower end was placed 
in an opening over the carrier-block, the case 
being in a vertical plane, and the spring s 
which closed the lower end being forced 
aside by the operation of inserting it. 

The cartridges then fell of their own 
weight into the grooves in the carrier-block, 
and were pushed forward by the bolts. The 
sliding weight w, and thumb-piece t, were intended to aid 
the fall of the cartridges, especially at high angles of eleva- 

Objections. — The objections to this feed were, that it 
did not work regularly for different angles of elevation, 
since the component of gravity parallel to the case varied 
with the angle of elevation. Also, the cartridges did not 
always fall parallel to the guide-grooves, and hence jam- 
ming was liable to occur, and in very rapid firing the car- 
tridges did not fall quickly enough to supply the barrels. 
For these reasons a second feed was introduced. 

The Bruce Feed. — This is a gravity feed, but is in- 
tended to force the cartridges to fall parallel to the guide- 
grooves and hence avoid jamming. It consists, Fig. 352, 
of an upright bronze standard, a, to which is pivoted a 
swinging piece, b, having two grooves in it. Below the 
grooves is a fixed mouth, c, and below this a wheel, d, turn- 

Fro. 351. 



ing freely on its axis. When in use the feed is inserted in 
an opening in the breech-casing directly over the carrier- 
block e. The paper box containing the cartridges, the 
top being removed, is placed in 
the fixed standard a, with the heads- 
of the cartridges to the rear. The 
heads of the cartridges engage in 
the grooves of the swinging-piece 
b, and the paper box may then be 
pulled off. In the position shown in 
the figure, the left-hand column of 
cartridges passes at once directly 
into the fixed mouth c, and as each- 
cartridge strikes the wheel d, its 
weight causes the latter to revolve 
and present a new groove for the 
reception of a cartridge. The car- 
tridges thus delivered to the wheel 
d are in turn 1 carried round by it 
and deposited in the grooves in the 
carrier-block e in the proper position. 
As soon as the left-hand column of 
cartridges is exhausted, the weight 
of the right-hand column causes the 
swinging-piece b to rotate to the left, 
and thus brings the right-hand col- 
umn over the fixed mouth c. This 
operation is repeated as long as the 
supply of cartridges is kept up. 

Objections.— This feed delivers 
the cartridges parallel to the barrels, 
and thus avoids jamming.; but as it 
depends on gravity, its action is 
variable for different angles of eleva- 
tion, as with the old tin case, and this objection has been 
overcome by the introduction of the Accles feed-drum. 

Fig. 352. 



343. The Gatling Gun — The Accles Feed — Advantages and Objec- 

This feed consists (Fig. 353) of a drum, with two heads 
of brass, connected by a sheet-brass casing. The distance 
•apart of the two heads is equal to the length of a cartridge. 

Fig. 353. 

The inside of each head is grooved in a spiral form, the 
spiral beginning at the centre and ending at the mouth or 
opening of the drum. The central part, a, of the spiral is 
removed, and its place occupied by the axis or pivot of a 
set of radial arms, b, which rotate about this axis. The car- 
tridges are inserted through the mouth c into the drum, 
the heads of the cartridges entering the spiral of one of the 
drum-heads, and the point of the bullet the corresponding 
spiral on the opposite drum-head. 

The cartridges thus rest in the spirals and between the 
radial arms. When in use, the feed-drum is inserted in an 
opening in the breech-casing, directly over the carrier-block 
■d, the opening c of the drum being down, and over the 


grooves of the block, and the planes of its heads at right 
angles to the axis of the barrels. Projections, e, are formed 
on the outer edges of the grooves of the carrier-block 
which engage with pins,/, joining the outer extremities of 
the radial arms of the drum, like the teeth of gear-wheels. 

When the crank k, Fig. 347, of the gun is rotated, the 
lock-cylinder, barrels, etc., revolve, and the projections on 
the grooves of the carrier-block cause the radial arms of 
the drum to rotate. These arms bearing against the car- 
tridges in the drum force them along the spirals toward the 
opening c, from which they are delivered to the grooves- 
of the carrier-block parallel to the latter. 

Advantages and Objections. — This drum feeds the 
cartridges without the aid of gravity and is hence a positive 
feed, and is independent of the angle of elevation. 

As it is driven by the carrier-block, it supplies the car- 
tridges as fast as they are needed, and thus the feed is per- 
fectly regulated ; and as the cartridges are guided by the 
spirals, they are delivered in the proper position to the 
carrier-block at all angles of elevation, and jamming is 

The objections are the weight of the drum, and the ex- 
tent of its surface exposed to hostile fire. A bullet striking 
the drum would render it useless. For these reasons a new 
feed has recently been introduced. 

344. The Gatling Gun— Latest Improved Feed. 

The latest feed introduced has a small surface exposed 
to fire, is independent of gravity, and can therefore be used 
with equal facility at any angle of elevation, and it is cheap 
and light. 

Long strips of tin or any cheap flexible metal, Fig. 354, 
have tongues or slits, a, punched in them, one end of the 
tongue being left attached to the strips, and the other 

These tongues surround the cartridge and hold it in 
place on the strip. The small rectangular slots b, are 
punched completely through, and in these slots fit the rims. 



of the cartridge-cases, thus preventing any side or longitu- 
dinal motion of the cartridges with respect to each other. 



a o a o o 0^,0 00000 

u IK 



Fig. 354. 

A hopper, a, Fig. 355, is hinged to the frame which sup- 
ports the gun, just over the carrier-block, and this hopper 
has an opening, b, on the left side through which the strips 
holding the cartridges are fed . This opening is narrow in 
front and wide in rear, in order to prevent the cartridges 
being introduced with the wrong end to the front. Below 

-(c) (oJ <°J (9) fe) l°J (?) to 


the opening b is a shelf, c, so shaped as to guide the car- 
tridges and strips into the opening. Above the shelf is a 
flat spring, d, which presses the cartridge-strips down as 


they pass through the opening. A wedge, e, projects from 
the opposite side of the hopper and, acting on each car- 
tridge in turn, forces it out of the strip, the tongues a, 
Fig. 354, bending downward into recesses provided for 
them. / is the carrier-block, provided with projections 
which act like the teeth of a wheel upon the cartridges, 
.forcing the strip to the right. 

When in use the strip containing the cartridges is 
pushed into the opening b of the hopper. The crank is then 
rotated, which causes the projections on the grooves of the 
carrier-block to act upon the cartridges, forcing the strip to 
the right through the hopper. This action brings each 
cartridge in succession against the point of the wedge e, and 
the action of the wedge forces the cartridge out of its hold 
on the strip by bending downwards the tongues a, Fig. 354, 
and the cartridge is deposited in the groove of the carrier- 
block, the empty strips passing out at the right. 

345. The Gardner Gun— Parts — The Barrels— The Casing — The 

Parts. — The parts of the Gardner gun are 

The barrels ; 

The casing ; 

The bolts ; 

The firing and extracting mechanism ; 

The cams ; 

The feed-valve and guide. 
Barrels.— There are two barrels, a, Fig. 356, which are 

Fig. 356. 

parallel and have their axes in the same horizontal plane. 
They have no motion, and are loaded and fired by the action 
of the bolts and firing mechanism. 



The Casing. — This is of bronze, the front part, b, being 
cylindrical and forming a support and protection for the 
barrels. Two openings, b' ', are made in the top and bottom, 
to permit a current of air to circulate around the barrels 
and keep them cool in firing. The rear part, c, of the casing 
is box-shaped and contains the mechanism. It is closed at 
the top by a cover, d, which is hinged to the forward part 
of the casing, and secured by a screw on the neck of the 
cascable, and may be raised, thus allowing the mechanism 
to be seen and readily removed. 

The Bolts. — -There are two bolts of U shape, Fig. 357, 

Fig. 357- 

one for each barrel. One side of the U has an arm, a, ex- 
tending at right angles to its length, and this arm forms the 
bolt proper, and carries the firing mechanism, and the ex- 
tractor, b. The U-shaped part of the bolt has a recess, c, into 
which the surface of the driving cam (a, Fig. 360) fits, at a 
certain period of its rotation, and it has also a projection, d, 
which at the proper period in the rotation of the cam, bears 
against its exterior surface. The sear e, projects in the recess 
c, and is acted on by the cam, when the latter enters that 
recess. The bolt as a whole has a backward and forward 
motion in the casing, running on the truck-wheel /. g is 
the cocking-lever, whose action will be explained. 

346. The Gardner Gun — The Firing Mechanism — Action— The 
Extracting Mechanism. 
The Firing Mechanism. — This consists (Fig. 358) of a 
hring-pin, h\ spiral main spring, z; cocking-lever, g\ sear, 



e; and sear-spring, j. The firing-pin has a collar, k, in front, 
and a toothed sleeve, /, in rear ; the latter sliding longitudi- 
nally along the firing-pin. The firing-pin terminates in rear 

Fig. 358. 

in a head, m, fixed to the pin ; n is the main-spring com- 
pressor, and the cocking-cam. 

Action of Fihing Mechanism. — In the position repre- 
sented in the. figure, the firing-pin is cocked, but the main- 
spring is not compressed. The head, m, of the firing-pin, is 
engaged with the sear, e. As the bolt is moved forward by 
the cam, the cocking-lever, g, moves with it, and the lower 
end of this lever bears against the main-spring compressor 
n, thus causing g to rotate, and acting by its teeth on those 
of the sleeve /, the latter is forced forward, compressing the 
main spring h, since the firing-pin is held by the sear e. 
When the main spring, h, is fully compressed, the cam a, 
Fig. 360, enters the recess c, Fig. 358, in the bolt, and press- 
ing on the sear e, releases it. The firing-pin then moves 
forward through the sleeve, under the action of the main 
spring, and fires the cartridge. 

As the bolt moves backward under the action of the 
cam, the lower end of the cocking-lever, g, bears against the 
cocking-cam o, and the firing-pin, by the action of the teeth 
of the cocking-lever on those of the sleeve, is forced to the 
rear till its head, m, catches over the sear. 

The Extracting Mechanism.— This consists (Fig. 359) 
of a hook-shaped extractor, b, on the end of the bolt a, which 
rides over the rim of the cartridge-case s, as tne latter is 



forced home, and withdraws the empty shell as the bolt moves 
backward. The ejectors are two levers,/, pivoted to the 

, ,b 


Fig. 359. 

sides t of the casing, the rear or bent ends, q, of which are 
struck by lugs, r, on the bolts as they move backwards. The 
cartridge-case being held by the extractor b, the end, u, of 
the lever, strikes the case, disengages it from the extractor, 
and throws it out of the casing. The ejectors also act as 
stops, to prevent the cartridges from dropping through the 
openings in rear of the barrels, when fed down by the valve. 

347. The Gardner Gun — The Cams — The Feed-valve and Guide. 










Fig. 360. 

THE Cams. — Motion is given to all the parts by two 
cams, a, Fig. 360. These cams are attached to three steel 
disks, b, at opposite extremities of a diameter, and the whole 
caused to rotate around the axis c by the crank d. As rota- 
tion continues, each cam acts against the U-shaped portion 
of its bolt, pushing it forward, and holding it motionless 
while firing occurs ; then moving it backwards, and holding 
it motionless while loading occurs. Firing and loading take 
place when the cams are in prolongation of the axis of the 



arm of the bolt carrying the firing-pin, at which time the 
direction of the force of recoil passes through the axis c of 
the cam-disks, and hence there is no tendency to rotate. 
The bolts are motionless for about \ of a revolution of the 
cams, to allow for hang-fires. 

The Feed-valve and Guide.— The feed is arranged 
as follows: A vertical bronze guide, g, Fig. ,361, resembling 

Fig. 361. 

the Bruce guide already explained lor the Gatling gun, 
but without the wheel, is fixed to the casing in rear of the 
barrels,- and holds the cartridges as previously explained. 
Below this feed-guide, the casing is perforated with two 
holes, for the passage of the partridges, and below these holes 
is the feed-valve, v, Figs. 362 and 363, which is a flat plate 
having two holes corresponding to those in the casing. 
This valve slides at right angles to the barrels, and is driven 
by a fork-shaped lever, /, which receives its motion from 
the bolts d, as they move forward. By this arrangement the 
cartridges drop from the feed-guide g, through the holes in 



the casing, and these holes are alternately opened and closed 
by the feed-valve v, as it moves to the right and left. When 
in the proper position, one of the holes in the feed-valve v, is 
in prolongation of the corresponding hole in the casing the 
other hole being closed, and the cartridge drops through, 
and is forced by the bolt into the chamber. The hole over 
the other barrel is then opened, and a cartridge drops, and 
is forced forward into that barrel. The details are best 
explained from the gun. 

Fig. 362, 



Fig. 363. 

The assembled mechanism is shown in Figs. 362 and 363. 
a the barrels, b the casing, c the breech-cover, d the bolts, 
e the cams, e' the disks, v the feed-valve, / the feed-valve 
lever, / the ejectors, h main-spring compressor, i cocking- 
cam, g feed, 7' cocking-lever. 

348. The Maxim Automatic Machine Gun — General Principles — 
Action of Mechanism — Advantage — Parts. 
General Principles. — The Maxim automatic machine 
gun is so constructed, that on firing a single shot, the force 


of the recoil is utilized for opening the breech, extracting 
the empty case, and effecting the various operations neces- 
sary to reload and again fire the arm, or prepare it for 
firing ; so that after the gun has been once fired, all these 
operations are performed automatically, and the gun con- 
tinues firing with great rapidity so long as the trigger 
remains pulled, and the supply of cartridges lasts. 

Action of Mechanism. — The breech mechanism is oper- 
ated by hand to insert the first cartridge in the barrel, and 
the trigger is then pulled. The pressure of the powder- 
gas on the breech-block, causes the latter, with the barrel, 
to recoil. During this recoil, the breech is opened, the 
empty cartridge case extracted, the firing-pin cocked, and 
a loaded cartridge brought into position to be thrust into 
the chamber. The energy of recoil not consumed in the 
above operation is stored up in a spiral spring, which by 
its reaction causes the barrel to return to the firing posi. 
tion, forces the loaded cartridge into the chamber, and 
closes the breech. The moment the breech is closed, the 
gun is fired automatically, if the trigger be held in the 
pulled position. The rate of fire is about 660 rounds per 

Advantage.— ^The great advantage of this gun is, that 
being automatic in its action, the aiming is not interfered 
with by the operation of a crank or other device to work 
the mechanism, and hence it can be pointed readily in any 
direction, and the direction chaqged with great facility. 

Parts. — The gun consists practically of two parts — a 
redoiling, and a non-recoiling part. The recoiling part 
embraces the barrel, the lock, the crank, the breech-block, 
and an inner frame with guides and bearings, on which 
these parts move. The recoiling part may be considered 
the gun proper. 

The non-recoiling part consists of a casing and two side 
frames, in which the recoiling part moves. 

349. The Maxim Automatic Machine Gun — The Barrel and Frame 
— The Breech Mechanism. 

The Barrel and Frame.— The gun has a single barrel, 









a, Fig. 364, attached to the inner frame b, and is an ordinary 
rifled one of the desired calibre. It 
has bearings at c and d, which rest 
in corresponding supports in the 
bronze casing, and on these bear- 
ings the barrel slides back and 
forth in action. The frame b is 
open at the top and bottom, and 
resembles a box. This frame car- 
ries the breech mechanism, and 
hence the latter moves back and 
forth with the barrel and. frame, 
and has also motion with respect 
to the frame, as will be explained. 
Near the rear end of the frame, the 
crank-shaft e passes through both 
sides, and has a motion of rota- 
tion in the frame. On the right 
hand side, this crank-shaft pro- 
jects, and upon it is fixed a bent 
lever, //', of the s